Depends on what we consider crazy or oddball, I guess...
The game that actually made me go WTF is The Adventures of Ninja Nanny and Sherrloch Sheltie. It's hard to explain what is this... thing about, it's like an interactive storybook for PC (Win 3.11 era), full of the most off-the-wall humour, weird voice acting, clipart visuals, public domain video clips, absurd plot events (is there even a plot?), the whole thing feels like an absurdist joke... yet it's apparent that the devs were doing their own thing, and it's not a try-hard attempt at weirdness or "random humour". It's really, really weird, probably the weirdest such thing made in the West.
Very close to the Ninja Nanny is an Amiga classic Weird Dreams, about a guy who's under narcosis during brain surgery and gets through some really surreal setpieces. You start in a cotton candy machine, then you play ball with little girl with big knife and slasher smile. The ball has mouth fulll of sharp teeth, by the way. Later, during a country fair, you fight a huge wasp... hitting it with a fish. Et cetera, et cetera.
Another game that really quirks me because it doesn't try to be weird, yet it is, is Raising Dead, obscure first-person shooter with some really weird things like levels filled with poison mushrooms that hurt you if you step onto them, skulls that bite you (in the ankles, I guess?), dudes who like Russian boiars with muskets etc. You fight using halberds, axes, ancient muskets, ak-47 and magic wand. Oh, and it's also a part of series of games, the others are called Old Gold and Dungeons of Kremlin, they both feature the mushrooms, skulls, boiars etc. So those were parts of the design from the very beginning!
There's also a ton of weird indie/shareware games, done by people with really eclectic tastes or just plain weird. Vasiliy Zotov's works, for example, or pre-Hotline Miami games from cactus.
