First of all I would like to say that I believe in God and demons and angels (just to make it clear) but not the way most people do it. I believe that they are here and watching us, but I don't believe in differences between religions, because we all worship just one same God no matter what his name is called . But I really doubt that this has a lot to do with this so I will start with my lesson
The case like the one you described happened to one of my best friends (and yes I believe in every word he said). He said he "woke up" one night and saw a dark shadowy figure standing above his bed and staring at him. He decribed this beeing as a tall, strong "man/demon" with black and strong wings and horns. He said that the beeing wasn't hostile at all but still it wasn't very pleasant to have something like that in his room. He told me he wasn't very afraid but he just could not move or talk and that his loudest "scream" was just a silent whisper. And the "beast" was there for some time and than just vanished from the room.
I was the only person he said anything about that. He was a religious man, but not religious like you and me, he was a Satanist. Now he is some sort of an ateist (I'm just writing this so you can be sure I'm not making this all up but it is not that important for the subject) but he believes in forces above people, but just does not worship any of them. And both of us often give time to explore and investigate supernatural and paranormal phenomenas and even to gather some informations how to induce those phenomenas (we are not summoning the demons or something, the thing we tried to induce is described in the next part of the text, read it carefully).
(sorry for the long intro, I hope you don't mind)
Anyway, when he explained me what happened I said I will do my best to help him find out what was that... In the conclusion we both came to the simplest anwser (and it is probably the best one), LUCID DREAMING, in which you have to get to the state of mind in which you are asleep but completely aware of the things you see and do in your so called "lucid dream".
But the process to reach this state is often mistaken and you get to an effect of something called "SLEEP PARALYSIS, and I believe you expirienced this so called "sleep paralysis". That is the state in which your body is asleep, but your mind is awake, you can't move and most people complain about "demons, monsters and creatures" that are actually just hallucionations.
I tried to induce both of the states myself, and I have to tell me that that can really be the anwser. Lucid dreaming is actually one of the best things I expirienced in my lifetime. Sleep paralysis on the other hand is not the best feeling but can be pretty fun if you are aware that you are expiriencing it. When I induced sleep paralysis for the first time I heard all kinds of movements in my room, saw shadows dancing and heard sounds that can be compared to breating. On the most of the next induced sleep paralysis I expirienced unstandable heat and increased heart rate.
When you get in this state of mind you can easily wake up by holding on your breath. So my suggestion to you if something tries to "possess" you again try to hold your breathing for like 10 seconds before you start chanting and praying
That is just my oppinion and I would be really happy if you do some reasearch on lucid dreaming and sleep paralysis, because if you do you will notice that most of your symptoms match to both of those states.