"demonic possession isn't a belief unique to Christianity."

That is not the point. You may attempt to discredit Christianity by diluting it with other so called religions over this subject. Believers are dealing this on a daily occurrence all around the world.

"Second, whether it lends credibility to Christianity or not is irrelevant to me"

Honestly, I think your mind is made up regardless of any "scientific" outcome or lack there of. However, this is beyond scientific study.

"Third, there are a theoretically infinite number of explanations for any and all phenomena."

Remember, there are countless Christians around the world dealing with this very issue. You may start with them if your pride isn't too big. I will warn you though. Being at an exorcism isn't a pretty site and not a pleasant experience. Then those who perform these exorcisms are harassed spiritually afterwards and if not them..then their families. I know, because I been through it a little.

"Fourth, if there were evidence in favour of demonic possession"

It's not a cut n' dry ... A to B, or dot to dot method of understanding and discovery.

Demons are disembodied spirits that require a host to take possession. Without a host, they are powerless, but they don't go away. When they take possession, they can do all sorts of things such as super natural strength, increased knowledge, so who knows but it's usually beyond human capabilities.

My advice to you after all, is to stay away. Because you and others like minded don't know what you would be getting exposed to. Because, you don't believe in God and His son Christ, you are not super naturally protected and very vulnerable.

Say what you want to say here and disagree all you want and leave it at that...but don't go chasing something that can destroy you.