Here's a number of recommendations; see if any of them suit your fancy:
Earth Defense Force. Imagine if a B movie about an alien invasion was turned into a third person shooter video game. That's pretty much what it is. Not the weirdest thing ever, but certainly quirky. The characters that talk on the intercom during your missions are constantly saying really stupid stuff like, "It's the pinnacle of evolution," or "You can defeat it by attacking!" Also, giant ants, robots, and godzilla things, ragdolling everywhere, and more explosions than you can shake a stick at.
Oh... Sir! is also fun, and pretty cheap. You try to defeat your opponent by slinging better insults than them. It seems kind of like a joke of a game, but the mechanics are actually pretty solid despite their simplicity, so it can still get competitive. Oh, and you'll often end up with some pretty weird insults, which is why I mention it in the first place.
Octodad: Dadliest Catch is quite strange. You play as an octopus masquerading as a normal dad guy. You have to accomplish various tasks whilst battling the hilariously difficult controls, which usually results in flailing your octo-limbs wildly and not quite doing what you're supposed to be doing. Pretty sure there's a co-op mode where you can split the controls and make life even harder (and sillier) for yourself.
West of Loathing is an incredibly absurd singleplayer RPG, and I honestly can't recommend it enough if you want laughs. It's stuffed full of jokes from beginning to end, and seemingly prides itself on being as ridiculous as possible at every juncture. Not a game you can play WITH friends, but it's certainly still fun to spectate.