If it's a PC and not one of Human, Dwarf, Elf, Gnome, Hobbit, Part-Elf or Part-Orc it's an oddball.what makes a race an oddball to you anyway?
And oddballs there have been, over the years: I've DMed as PCs two Leprechauns, a Dryad, a couple of Drow, a Centaur, a Gnoll, a Part-Deity(!), a minor Devil, and a small boatload of strange and varied inter-species crossbreeds e.g. a character who has both Orc and Elf in its recent ancestry and is thus a Part-Elf and Part-Orc at the same time, a Human-YuanTi cross, etc.
The most bizarre of all was a character who ended up being a cross between a Skulk and a Frostman. The player here got into the oddball charts and for a while I thought she was never going to stop; the dice just kept taking her from one table to another, each less likely than the last.