I've been taking a good, long look at demonology as well as exorcism.  Fascinating subjects really as they relate to both religious and cultural views.  I am certainly no expert on anything concerning the paranormal but I can throw out a couple of things that may answer your questions.

First up, the very definition of ghost and demon.  It seems widely believed in paranormal circles that a ghost is some sort of "energy" that used to be a living person.  A demon, however, seems to be an entity that was never human.  The demon experience, or possession, is treated very differently.  That's where the exorcism and the like come in.

Here's a link to Keith Johnson's (one of the twin demonologists shown on TAPS) website.  It's a long Q&A that may explain common beliefs associated with demons:

http://www.nearparanormal.com/desk.html

What happens if the family experiencing some event isn't Catholic?  Well, they would most likely go with their own clergy.  Here's a link over at wiki and they do talk about the views of many religions:

http://en.wikipedia.org/wiki/Demonology

To answer why they "always" call a Catholic priest…because they've probably researched the family before going to the home so they know the religion before going in.  Since they are most likely Catholic themselves, they accept the case.  If a different religion, they would probably just get the family in contact with local churches willing to help.

The most interesting question…what would an atheist do?  Well, good question.  Since religion is removed from the equation…which is really needed it seems when pertaining to demons, the atheist, I would imagine would resort to perhaps modern day medicine and/or science.  It stands to reason if the atheist is not looking for supernatural answers (no insult to any religion), he will not find any.  The atheist would generally look for medical treatment to treat symptoms that a demonologist may view as "signs of possession."  If he hears strange noises in the home, perhaps an exterminator would be called.  Maybe even a plumber.  If something "moves on its own" maybe a contractor to look at the foundation of the house.  The list goes on and on.  I would think that the atheist would seek help from various professions in which he knew and trusted. 

Again, I'm just throwing things out there.  I hope it helped…

dianebk said:

All of the shows that I have viewed on all stations refer ghost-hunters, and demon-encounters to catholic priests. What happens if the family or person is an atheist or a religion, other than Catholic? I'm interested in call the Rabbi! Diane

Just found this and I can't get to load: Listen to Disturbed Paranormals March 25 internet radio show about Possession possessed demonic author and Rabbi Gershon Winkler writer books Interview …

Thanks Diane, really made me think about how other religions and athiests handle exorcism.  Off to check out the links Revenant posted.

Admin: Edited to fix link