I would like to see more of a spiritual demon than a physical one, that can possess creatures in various ways. Maybe certain types of humanoids are immune to certain demonic attacks or certain types of demons/devils, or humanoids that have gone through certain religious rituals (ie baptism, communion, ritual scarring, etc.) are immune to the weaker demons, but subject to the stronger ones higher up in the hierarchy.
I would prefer made up names for fantasy versions of demons, instead of using real world names from various religions, as personally I think that's a little too creepy to use real world names.
I would like to see some rules on exorcism, as I think that would add some nice flair to a game. Many real world cultures have exorcism rites, so maybe various rituals with the same goal (free the person from their grip) would be good.
Demonic possession and exorcisms are scary (see movies dealing with the topic, or real world examples) as it represents a call to an older time and older belief, where today in our "civilized world" demons are explained away by science and abnormal psychology as a general belief, even though many people still believe in their existence.
I think the scariest thing as a possessed person would be knowing they are there and not be able to do anything about it, or remove them, as they have taken control of your body. I think that another humanoid, or humanoids would have to perform the ritual as you can't remove them yourself once they are already in place.
Also once removed, demons will want to return to their original host, and when they return, they will bring more of their kind with them, normally much stronger, to occupy the same host again. You can clean the house, but they will always want to return. So for one that has had an exorcism, they must stay on the watch, and live by the tenets of their religion to not become possessed again.
Also spiritual attacks on those that are trying to perform the exorcism would be good. Recurring nightmares/night terrors, the loss of certain motor functions during the attack or waking up from dreams, hearing growling evil multiple voices, having evil thoughts placed in your mind, curses that must be resisted, being haunted by them, and having general "bad luck" from demonic influence in the world.
For those performing the exorcism perhaps there are certain names when uttered thwart certain demonic attacks (this would be different for each religion). Normally the name of the God(s) they worship, or certain quotations from religious texts would be examples based on whatever fantasy religions would be made up for it. Normally quotations about exorcism would be used, but also other ones work as well.
Laying on of hands, prayer, fasting, reading religious quotations, holy water, holy oil, smoke, and other similar things would be needed.
(Sorry if this is too much real world stuff, but I have had some weird experiences in my life in this area with my brother).
For example, I don't think demons should ever be able to be "killed." You can defeat them by scaring them away (names of God, religious text quotations, prayer, fasting, etc.) or removing them from whatever host they are occupying at the time by exorcism.
Just some thoughts, though to be honest, I normally stay away from books dealing with the topic.
Have fun coming up with ideas.