Asking “science or religion? which is right?” is a bit misleading. It is not the case that all religions believe in demonic possession, and so science and religion need not conflict here in all cases. I did not believe in demonic possession when I was religious, and I do not believe in demonic possession now that I am irreligious.
@Hibernate It does not follow from believing in God that you must believe in demons. This is a false choice. You seem to be reasoning this way:
1) Everything has an opposite.
2) I, @Hibernate, believe in God.
3) Therefore, I must believe in the opposite of God.
For some reason, you then take the opposite of God to be demons (as opposed to Satan or some other non-divine entity). This decision is not explained, but we can leave that aside. Your first premise, after all, is suspicious enough.
What is the opposite of a fish? What is the opposite of a lightbulb? What reason do we have to believe that everything has not just a formal or conceptual opposite (which I could agree to given certain qualifications), but an actual or substantive thing which is that opposite?
You might deny, of course, that you are reasoning in the way I suppose above. But if that is the case, we would still need a reason why belief in God must bring belief in demons along with it. The latter does not necessarily follow from the other without the assumption of some further principle. The principle I have ascribed to you above is common and at least superficially plausible. It also is strongly suggested by what you have written. Should you have some other explanation for your position, however, I would be interested to see it.