Obsession and addiction often go together: we tend to get obsessed with whatever we’re addicted to, and can't stop thinking about it. Intrusive thoughts are also in this category - we don’t want them any more than we want an addiction, but by their very nature, they dominate our thoughts, and thus become an obsession.

All of these have a common origin. 

All Obsessions Start With Something Good, and then Twist It

Evil defines itself by the absence of God, just as darkness defines itself as the absence of light. Satan cannot create anything; all he can do is pervert something that God made, and intended for good. 

So if evil itself is an inversion of something created to be good, then nearly everything 

God created for our pleasure and enjoyment can also become evil, or sinful, if we make it our highest aim or focus. 

Obsessions and Addiction are Placing Anything Before God

God's very first commandment to the Israelites in the Old Testament was to have no other gods before Him (Ex 20:3). The Israelites broke this commandment over and over in a very literal sense, worshipping false gods first that they'd grown up with from Egypt, and then the false gods of the nations they encountered in the wilderness and in the surrounding nations of the Promised Land. 

Today, most of us don't literally worship false gods, per se (though that's becoming more prevalent too). Rather, we make some desire or worry or need or love the focus of our lives, instead of God. 

C.S. Lewis wrote that romantic love (a very common substitute for God) "ceases to be a devil only when it ceases to be a god." The same would go for any other positive good that God created for our benefit--all could become something we seek after, more than we seek after God. That's really a prerequisite for any obsession or addiction. 

Jesus told us that if we'd seek Him and His kingdom first, everything else would be added to us (Matt 6:25-34). That's not just our needs, either. God is the giver of every good and perfect gift (James 1:17). If we make Him our primary delight, we'll get the desires of our hearts thrown in (Psalm 37:4). If we're abiding in Him first, we can ask whatever we desire, and it will be done for us (John 15:7). That's what it means, that if we find our lives (make that our primary focus), we'll lose it, but if we lose it for His sake, then we'll find it (Matthew 10:39).

The problem is, most of us don't actually believe that. 

One of my favorite fictional stories is the Superman myth. It's such a clear parable. (Also, apparently the creators of Superman were Jewish, not Christian, but they based the character of Superman on Moses and Samson of the Old Testament, as well as the prophecies of the coming Messiah. Some of the earlier Superman movies were conscious of the Christ symbolism, as well.) Lois Lane fawns over Superman, while ignoring Clark Kent—not realizing that Superman remains elusive to her only because it's clear that she doesn't really love him; she only loves what he can do for her. If she'd only choose Clark, she'd get Superman thrown in.

I think God is exactly like that. He loves us, and He longs to bless us (Psalm 103:1-5), but He wants our hearts, not our actions. He wanted a relationship with Israel, after bringing them out of the wilderness--but they were afraid of Him, and asked Moses to just be His mouthpiece and relay to them what He said (Ex 20:18-19). Even after that, God asked Moses to take seventy of Israel's elders and bring them a little way up the mountain so that they could eat and drink in His presence--even though He was at a distance, He wanted them to catch a glimpse of Him (Ex 24:9-11). He wanted to have dinner with His family. God later made this part of how the Israelites were to worship: they were to bring all their burnt offerings, sacrifices, tithes, and heave offerings of grain to the place of worship, and eat it together in His presence (Deut 12:5-7). He blessed them with increase, and as their act of worship, He wanted them to have a big feast and enjoy it. All He asked was that they invite Him to the party! 

Understanding how much God loves us is really the key to faith--faith works though love (Gal 5:6). If we don't understand how much He loves us, we aren't going to trust Him to take care of us and meet our needs (Isaiah 26:3). That's why we'll try to take matters into our own hands, attempting to meet our own needs (as an anxious primary fixation—not as the side benefit of doing our work well for the purposes of glorifying God, Col 3:23-24). But if we do truly put God first, it’s the antidote to all anxiety, addiction, and obsession.

Willpower ("The Law") Won't Work. That's the Whole Point.

Paul describes in Romans 7:14-24 what happens when we try to suppress or control any obsessive or addictive tendency: "For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do… For I know that in me (that is, in my flesh) nothing good dwells; for to will is present with me, but how to perform what is good I do not find.  For the good that I will to do, I do not do; but the evil I will not to do, that I practice.  Now if I do what I will not to do, it is no longer I who do it, but sin that dwells in me.  I find then a law, that evil is present with me, the one who wills to do good.  For I delight in the law of God according to the inward man.  But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members.  O wretched man that I am! Who will deliver me from this body of death?  I thank God—through Jesus Christ our Lord! So then, with the mind I myself serve the law of God, but with the flesh the law of sin."

This describes the experience of every yo-yo dieter, every sugar addict, every alcoholic, or everyone addicted to any other substance or behavior. Paul repeats the same concept in Galatians 5:17: "For the flesh lusts against the Spirit, and the Spirit against the flesh; and these are contrary to one another, so that you do not do the things that you wish." You might be able to exert willpower against those things for a time, but the very act of denying yourself actually makes the desire for the thing denied grow stronger. That's what the Old Testament law was designed to do--to make us aware that we were incapable of keeping it, apart from God's help (Romans 7:5-6). Paul addresses the next logical objection: "What shall we say then? Is the law sin? Certainly not! On the contrary, I would not have known sin except through the law. For I would not have known covetousness unless the law had said, 'You shall not covet.' But sin, taking opportunity by the commandment, produced in me all manner of evil desire. For apart from the law sin was dead. I was alive once without the law, but when the commandment came, sin revived and I died. And the commandment, which was to bring life, I found to bring death." (Romans 7:7-10). This is just the way of our flesh: it rebels against any rules placed upon it--even if the rules are neutral, or if you know they're for your good and will achieve a desired end, and even if they're self-imposed. This is the whole concept behind any type of “forbidden fruit.”

That phrase itself alludes to the single fruit in the garden forbidden to Adam and Eve, from the tree of the knowledge of good and evil, though God had given them so much abundance elsewhere (Genesis 3); the very fact that it was forbidden called their attention to it, making it more attractive. (This is also why, for instance, a perfect recipe for insomnia is to try to will yourself to sleep--the harder you try, the more wide awake you'll be. It's also why trying to suppress any intrusive thoughts will have the opposite effect. “Don't think about a pink elephant"--see, what are you thinking about right now?) 
Fortunately, the story doesn't end with Romans 7, though. Paul is tracing the story of God's relationship with humanity through successive covenants. Before the law came, He did not impute sin to men yet (Romans 7:8-9), which is why after Cain murdered his brother, God actually protected him (Gen 4:13-15). Yet after Noah's covenant (which was the first to include a command not to murder), then murder was to be punished as sin (Gen 9:5-6). At this point it was the only sin to be called out, though, so it was the only sin that carried punishment, until the Mosaic covenant made the rest explicit. This is the law Paul describes in Romans 7, and the entire Old Testament dramatizes the fact that men are incapable of being righteous by works; that was Paul's point. God wanted us to know that we're incapable in our flesh, so that we'd be aware that we needed a savior to do it for us.

That's why Romans 8 follows Romans 7. Romans 7 is all about us (our "flesh") trying to keep the law--any law--by ourselves. By contrast, Romans 8 describes what happens when we have help from the Holy Spirit. "For the law of the Spirit of life in Christ Jesus has made me free from the law of sin and death. For what the law could not do in that it was weak through the flesh, God did by sending His own Son in the likeness of sinful flesh, on account of sin... For to be carnally minded is death, but to be spiritually minded is life and peace. ...So then, those who are in the flesh cannot please God. But you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you." (Romans 8:2-11). This is about salvation, yes, but it's also more practical than that. Those of us who are saved can still choose to walk in the flesh (by our own efforts) or we can surrender to God and walk by His Spirit, with His help. This is the main message of Galatians; Paul writes, "Did you receive the Spirit by works of the law, or by hearing of faith? Are you so foolish? Having begun in the Spirit, are you now being made perfect by the flesh?” (Gal 3:2-3). Obviously this is rhetorical--but it's clear that even those who have received forgiveness for their sins can choose to return to the efforts of their flesh, if they want to do so. But it will only produce bondage if they do. Paul writes, “Stand fast therefore in the liberty by which Christ has made us free, and do not be entangled again with a yoke of bondage” (Gal 5:1).

 Obsession and addiction is the compulsion to obey a master other than God. That's bondage. Paul writes, "Do you not know that to whom you present yourselves slaves to obey, you are that one's slaves whom you obey, whether of sin leading to death, or of obedience leading to righteousness?" (Romans 6:16).

How to Get Free: Walking By the Spirit

Paul's juxtaposition in Romans opposite walking in the flesh is walking by the spirit. But the big caveat is that we don't walk in the spirit by trying to walk in the spirit; If we try, if WE try, we're doing it from the flesh. That will never ultimately work, and will likely have the opposite effect eventually. That's how all works of the flesh are. We don't "ask God to do it for us," either, though, because He already did it! He can't give us again something He already gave us. Instead, our part is to acknowledge what Jesus did for us, and thank Him for it. Paul wrote in Philemon 1:6 that Philemon's faith became effective by the "acknowledging [of] every good thing which is in you in Christ Jesus."

And what has Christ provided?

• 2 Corinthians 5:17 says, "Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things have become new." (Past tense. This is ours in the spirit, but not necessarily in the flesh--we're to work this out in our souls and flesh, with God's help: Phil 2:12).
• Galatians 2:20: "I have been crucified with Christ. It is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me."
• 2 Peter 1:4: "By which he has granted to us his precious and very great promises, so that through them you may become partakers of the divine nature, having escaped from the corruption that is in the world because of sinful desire."
• 1 Corinthians 2:12-16: "Now we have received, not the spirit of the world, but the Spirit who is from God, that we might know the things that have been freely given to us by God... We have the mind of Christ."
• Phil 4:13: "I can do all things through him who strengthens me."
• 2 Timothy 1:7: "For God gave us a spirit not of fear but of power and love and self-control."

We also have the fruit of the spirit. We don't have to conjure it up (and indeed, we can't), but it's already ours: "the fruit of the Spirit is love, joy, peace, longsuffering, kindness, goodness, faithfulness, gentleness, and self-control." (Galatians 5:22).
We don't strain to live from this place; we thank God that it is ours already (Phil 4:6-7). Our labor now is only to enter that state of resting in what He has already done (Hebrews 4:11).

Satan contributes to obsessions and intrusive thoughts, of course--whether they originate with him or with our flesh, it's certainly his agenda to keep us in chains. But thank God, the power of Satan was sin--that was the Old Testament curse, and Jesus redeemed us from the curse (Galatians 3:13). The power Satan has over us now is only the power to deceive us. That's why Paul tells us that when Satan comes to us with lies, we're to fight back with the weapons God gave us, taking every thought captive and making it obedient to Christ (2 Cor 10:5). But they're God's weapons, not ours. In Eph 6:12-18, Paul enumerates them--they are truth (being well grounded in God's word so that we can recognize lies when we hear them, even and especially if they are half-truths), righteousness (understanding that we are righteous because of what Jesus did, not because of anything we do--and that we are righteous already, so can can come boldly before the throne of grace, and expect to receive help in time of need, Heb 4:16), peace (which guards our minds, Phil 4:7), faith (you can't have peace without faith, Isaiah 26:3), salvation (which also means we have the Holy Spirit living in us as our guide), and the sword of the Spirit, God's word. This is the offensive weapon; the only one Paul lists. The Holy Spirit will bring to our remembrance those scriptures we know, when we need them (John 14:26).

So the keys God gave us to achieve freedom are to remember that He gave us His Spirit, to thank Him that although we can't free ourselves, He freed us already--and to use the spiritual weapons He gave us to enforce what is already ours.

And then, go about the business of God's kingdom. Fixating on trying to solve your problem will only keep you stuck in the loop of thinking you can solve your problem. You can't; but He already did. We can trust Him for the full manifestation of that freedom, just like Jesus told us to trust Him to meet our physical needs (Matt 6:25-34). And he says we get those by going about His business, by seeking after something greater than ourselves. When we do that, Jesus promised that we’d get everything else thrown in.