My palms are incredibly ticklish! That was made quite clear back in high school which was the biggest reason my friends started to tickle me more and more as time went by. They would love to pin my arms down to a table and write on them with a pen. Drove me completely insane.
Same with my feet. At a party once, my friend sat on my legs as a joke and another decided to start drawing a picture of the road runner on my feet with an ink pen (don't remember why it was road runner) and it was the most incredibly ticklish experience I have had so far.
To this day, ink pens in the hands of particular people make me incredibly nervous.
As far as "odd" places, I don't have any that I can think of. However, I do have one spot in particular that will get a very...unusual reaction from me. But that's another story for another thread 😛