BroCalton,
Derek Prince has many sermons on casting out demons, he believed that Christian's (born again people) could be oppressed of the devil. His explanation was Chicago because he lived there at the time, he stated that did Mayor Daley and the police dept have control of every single area in Chicago? No, they did not.
And he likened that to a believer's life except that he asked, "Does the Holy Spirit have control of every single area of your life?" Not that any area of your life is demonized but in some Christian's lives, it is.
I think he tells the story in this sermon and I believe a LOT of your questions will be answered here:
Derek Prince - How To Be Delivered (From Demons / Evil Spirits) (1995)
https://www.youtube.com/watch?v=Ed8j33e8viE
(Greg, I didn't see this sermon listed on SI is why I posted the link. I'll take it down if you don't want it here.)
About the other half of your statement, I believe in the NT Jesus didn't minister to Christian's because there weren't any, but He did minister to God's chosen people and Matt, Mark, Luke and John is full of those who were oppressed of the devil and Jesus setting them free.
Ac 10:38 How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing all that were oppressed of the devil; for God was with him.
God bless,
Lisa