I'd say the oddest was steamed octopus. It was very hard to eat and I regret not putting anything on it because it was tasteless. I used to live near a place that sold nothing but buffalo burgers. They raised them there any everything. It was way out in the boonies and not very big or crowded, which is my favorite kind of place.
As far as homemade unusually taste, I like onion and peanut butter sandwiches.