That was my experience, although it would start where I would sense a very evil presence creeping up on me. I would try to force myself awake by yelling, but I could hardly get anything out and couldn't force myself awake. It was like I was awake and aware of everything around me yet still in a deep sleep. I felt paralyzed. I remember seeing the 'old hag', or 'the witch' as I called her, on some of the occurrences, but not always.
I've had that type of dream where I'm aware of everything around me but can't move. (BTW when this happens to me I usually see everything around me is dark and I try to turn the light on but it won't come on--does this happen in yours?). Sometimes in this type of dream I sense an evil presence though not always; sometimes I just sense myself panicking that I can't move (and perhaps the fear generated by this panic is what summons the evil presence?--evil seems to be drawn to strong fear and anger, in my experience). Hufford's book identifies this type of dream with a sleep state called the "hypnagogic state" that occurs during the transition between waking and sleep and vice-versa, as the mind and brain are adjusting to being in the dream state rather than the waking state:
The hypnagogic state is a state of transition in semiconsciousness between being awake and being asleep, and may be a form of sleep paralysis. Some experience visual and/or auditory hallucinations. Out of Body experiences may be experienced. See also hypnopompic state, a similar state between sleep and awakeness.
Many people have reported--and I've found this has worked for me--that when you feel paralyzed in this type of dream, you can break the paralysis by focusing your effort on moving a small part of your body, even your pinky, which breaks the hypnagogic state by reactivating your tactile awareness of your body and physical surroundings. I had a dream once where something invisible was trying to choke me, and in response in my dream I started instinctively trying to do a Kung Fu move I was studying at the time. It took me a few seconds of mentally trying to do the move before I "felt" myself doing the move in my dream, whereupon I woke up. Needless to say, I didn't want to go back to sleep for a while after that :) I had this overwhelming urge to grab a Bible, run to the church down the street, call my brother at 3 am, etc. I definitely know what you mean by a sense of evil presence, though fortunately I didn't visually see anything, which would've made it even scarier.