I've never had a demon-related nightmare, but when I was younger I I was terrified of demons. My mother had a close friend, a pioneer sister, who claimed to have had close experiences with demons (the urban legend of being in a school bathroom when a group of "worldly" girls held a seance with a ouija board was one she told) and, being a superstititous young JW, I became quite paranoid about the presence of supernatural entities able to maliciously manipulate our lives. Even the trailers of movies about demonic possession made me extremely uneasy, and I remember one night in ninth grade when merely holding a conversation about the movie The Exorcist had me looking back over my shoulder the entire bike ride home (conducted at around 2 am).
The ironic thing is that now that I'm out I find myself very intrigued by demonology and legends about malifecent spirits from around the world. I'm especially interested in vampire legends, which I think are a sweet aspect of European folklore - there are very rich and imaginative stories about vampires both ancient and modern. When you reduce the notion of demonology to just one more aspect of the dynamic and vibrant spiritual culture universal to just about every human society, it takes the fear out of you. You kind of learn to think of them simply as stories, just like any other fairy tale, and you can take from them whatever themes or lessons you find in them. There's no need to worry about any influence on your thinking, because you decide yourself how what you learn will influence you.
And that's a freedom you could never have in the JWs.