Demonic influence - a pastoral issue

Can people who have become Christians still suffer the lingering effects of demonic or occult activity from their past lives? Certainly this is a real issue for many pastors.

I have traditionally said that the victory of Christ on the cross over the powers was so absolute that Christians have no reason to fear demonic influence or even to inquire after it. Additionally, I think the charismatic movement has had a disastrous and disgraceful influence in evangelical Christianity on this very issue, causing people to fear quite unnecessarily and to doubt the power of the cross of Christ and to become fascinated with the very things that they should not become fascinated with (with all due and sincere respect to my charismatic brothers and sisters many of whom would acknowledge these kind of excesses anyway). My goodness, some of the silly things I have heard about ancestral spirits and the freemasonry etc etc!

BUT: is this really all there is to say? Let me take an analogy: Christians are not to fear sickness and death anymore because of their hope in Christ. And yet of course we still experience sickness and death and have to deal with them. Or: I know several Christians who have depression. Becoming Christian did not alleviate them of their depression though in some ways it has helped them to be better at managing it and more determined to and they do have assurance that they won't carry their mental illness into the resurrection body.

Now: can we make a parallel with demon possession here? Is it possible that merely being reassured about the victory of Christ over the powers and principalities does not mean freedom from the influence of malignant spirits of whatever kind? Is there a place for the Christian to seek deliverance from a certain kind of influence in their life just as they might go to counselling in order to help them with an addiction they have brought with them into the Christian life? And: what kind of action would help?