Edgy as in the definition you stated basically.
The jokes aren't exactly "dark" or that offensive (I'm saying "that" because Murfy literally asks you if you're mentally... yeah

) but they would make a white angry mom convulse on the floor if they heard it. I'd say most of the jokes are just "haha, funny sex joke" or "haha, globox is stupid!" that most of the time flop unless done right
I mean I laughed at some of them, like the Globox running into the Uglette cut-out, or the Murfy one where the manual says he needs to shut up before he's on an X-rated channel or something, but some of them are almost uncomfortable to sit through like the Begoniax and Razoff cutscene

... And the Globox is dumb jokes can be really hilarious, like all of the things he says whilst you're on the ship, but most of them can be annoying since he talks a little bit.. too much
And the rest of the humor is just randomness that I absolutely love. Everytime the Knaaren say "Make him write bad checks!" I always have a giggle or two. Or the one where Globox turns smart and he's talking about how superior he is. And, all of Andre's dialogue when he's in Globox's stomach is great, too.
The main point is; they're good at the humor, but they try to throw in edgy sex jokes or Globox jokes that drag on for too long, and they're honestly SUPER unfunny and irritating to sit through.