On the main Overdrive page (in the menu at the left side of the page) there are menus for some broad fiction and non fiction genres. Click 'more' to see Overdrive's genre list. They don't list all genres, but there are a few that may help you search.
You may also enter a specific genre in the quick search box. Don't be afraid to be specific or creative (Chicago mysteries, teen paranormal romance). The Overdrive search engine is pretty robust and may give you just what you were looking for!