There are not a lot of solid biblical books on the topic of demons and demon possession (there are, however, plenty of bad ones!). Here’s a good one worth mentioning: Satan Cast Out [Frederick Leahy (Edinburgh: Banner of Truth, 1975)]. This book is balanced, full of biblical references and summaries, Christ centered, and it is written from a Reformed point of view. One part asks – and answers well – the question: “Can a Christian be demon-possessed?” I’ve edited it for length:
“In the light of Scripture we are compelled to reject the view that the Holy Spirit and an evil spirit can co-exist in the same person. …When missionaries provide ‘examples’ of ‘believers’ being possessed, two questions immediately arise: Were the victims [truly] regenerate? Were they actually possessed? Passages of Scripture sometimes used to support this view prove no such thing. There is no reason to believe that the person ‘delivered unto Satan for the destruction of the flesh, that the spirit may be saved’ (1 Cor. 5:5) was demon possessed (which is also true of 1 Tim. 1:20). Those discussed in 2 Timothy 2:26 and said to be ‘taken captive’ by the devil ‘at his will,’ are not believers at all.”
“The Biblical doctrines of regeneration and the permanent indwelling of the believer by the Holy Spirit make demon-possession of a believer utterly impossible. We are not asking if a professing Christian can be demon-possessed, but if a [truly] regenerate person can be possessed. The answer to this question is firmly in the negative. A true Christian is ‘born again;’ he is a ‘new creation’ in Christ. He is part of the body of Christ and sealed by the Holy Spirit unto the day of redemption. He is permanently indwelt by the Holy Spirit. He is the temple of the Holy Spirit, and the evil principalities and powers cannot separate him from the love of God in Christ. The One in the Christian is greater than the one in the world. The Holy Spirit and an evil spirit cannot be joint occupants of the same heart. Believers are ‘in Christ’ and Christ is ‘in’ them. It is altogether impossible for those who are ‘Christ’s’ to be Satan’s. ‘We are the Lord’s’, and we can belong to none other. (cf. Jn 3:5, 2 Cor. 5:17, Eph. 1:23, Eph 4:30, Rom. 8:9, 1 Cor. 6:19, Rom. 8:38-39, 1 Jn. 4:4, 2 Cor. 6:15-16, Eph. 3:17, Col 1.27, 1 Cor. 3:23).
“The Christian cannot be demon possessed. Such a notion contradicts everything which the New Testament has to say concerning the nature of the new birth and the standing of the child of God. ‘It is impossible,’ says Martin Luther, ‘for Jesus Christ and the devil ever to remain under the same roof. The one must yield to the other – the devil to Christ.”