Can a Christian be possessed? 

The word possession is what we get hung up on.  Christians can be totally possessed by an evil spirit but not possessed. If someone has gone through horrific abuse and they switch to another personality, then that is possession. The devil may have a stronghold and reigns attached to you that is influencing you. 

Strongholds are mainly in believing lies about your identity and who you are in Christ. We believe the lies because the person does not know how to discern the good and evil quoted in Hebrews 5:13-14.