Well, I don't want to argue about terms. "Possessed" means owned. A Christian is not owned by Satan.
But a Christian can certainly be oppressed.
Let me explain.
Look at 1 Thessalonians 5:23: "Now may the God of peace Himself sanctify you completely; and may your whole spirit, soul and body be preserved blameless at the coming of our Lord Jesus Christ."
We are spirits. We have souls. We live in bodies.
When you became a Christian, your spirit became Christ's. Satan had owned you before this, but now the Holy Spirit lives in your spirit. As stated above, there is no room for light and darkness.
But your soul is another thing. Everytime you sinned in your former life, you gave ground to Satan. Now Satan--or rather his demons-- need to be kicked out of your soul.
The Holy Spirit does this as you walk in obedience to the Word of God. Some of these struggles are difficult! But you can take authority over the enemy and tell him to be gone, James 4:7-8. Do this out loud in Jesus name.
For example, suppose you are dealing with a habitual sin that seems to get the better of you more times than not. Suspect a demon stronghold in that part of your soul.
Here is what you do to overcome that enemy:
1. Repent of the sin that gave Satan a legal hold on you, James 4:7; Ps. 94:20; 1 John 1:9.
2. Address that demon specifically. Tell it out loud that in the name of Jesus you are resisting it and therefore it must leave, James 4:7-8.
3. Spend time in praise and prayer, James 4:8.
4. Ask God to seal that area of your soul with the blood of Jesus, and seal the door that was used to attack you.
5. Walk in obedience to Scripture. Make no provision for this sin ever again in your life. Psalm 85:8 warns us not to go back to things we have been delivered from.
If you do fall again, repeat the steps. Don't let sin rule over you, because Jesus has given you authority to rule over it! Romans 6:12
The third part of you is your body. I believe that some diseases are actually caused by demons. That is why when Jesus healed we often hear of people being delivered from demons. Discernment is needed. When praying for someone like this, ask the Lord to show you anything that needs to first of all be forgiven, and then any demon that you need to come against. James 5:14-15 talks about sin being forgiven in the context of healing.
I hope this helps. Like many Christians, I didn't want to believe that demons could oppress people, but I was wrong. There came a time in my life when I prayed for Christians--and they were delivered from demons. I had to correct my theology.