Eccentric or weird. In this phrase, a "crumpet" (a muffinlike pastry) is synonymous with one's head, and "barmy" means "yeasty." What do you think of John's strange behavior lately? I'm starting to wonder if he's a bit barmy on the crumpet.

One who is considered both intelligent and attractive, and is therefore sexually desirable. It's clear that she's trying to present herself as the thinking man's crumpet, always carrying around those books.