If you haven't read Limon de Campo's post Banana Land, you absolutely must.
I'm afraid I don't have any weirdo student stories to share at this point. In fact, I don't think I've had a truly weird student for several years. A bit eccentric, yes. Flat-out weird, no. One student who sticks out in my memory is the one who didn't know his own phone number.
Not so much weird as clueless and ignorant: An African-American friend of mine once had a student come to her office hours to ask her, "So, what's up with black people and watermelon?"
I'm in the mood for weird student anecdotes. Feel free to share them in the comments.