Sleep Paralysis is for sure my favorite oddity. I've not experienced it in 20 years and I miss it. It happened about once a year when I was young and into my early 20s. Mine often had weird noises and hallucinations and creatures floating around. The first few times it was rather scary but then I realized it was pretty neat. The trick I learned is to tell myself I just have to move my toe.
I've experienced it once or twice, and mine was the classic "can't move, malevolent presence just barely in the corner of your vision". Once, I think I was actually still half-asleep-ish, and trying to yell and my wife woke me up. Definitely not pleasant, even when I'm rationally aware of what's going on.
I've never seen the shadow man or anything.