They've already been mentioned, but The Dead Milkmen are exactly what you're looking for.

Peter Gabriel era Genesis was pretty goofy, as well as some of his solo stuff.

King Gizzard and the Lizard Wizard is pretty much the goofiest band known to man right now; especially if you listen to their earlier stuff like Cellophane or Vegemite.

Have you checked Nanowar (of steel) which is parodic metal ?

fine young cannibals, wall of voodoo/stan ridgeway.

Electric Callboy are very silly and produce excellent videos.

JBO, if you understand German.

Sparks. Best. Band. Ever.

I don't know if its 'silly' but Health runs a phone number, a discord, and subjects Johnny to a bunch of miserable shit for laughs I guess.

if ska counts, reel big fish

The Aquabats

Future Idiots.

Patent Pending.

TENACIOUS D! I unironically listen to their first album a lot lol. Weird Al, obviously. Suburban Lawns, the Aquabats, Reel Big Fish, Green Day (the album Dookie in particular), Presidents of the United States of America, Primus, Mr. Bungle, the Adicts, the King Kahn & BBQ Show, Nobunny, Weedeater, Spazz, Gravy Train!!!, the Pixies, GWAR, King Diamond, Busdriver, MF Doom, Talking Heads

Your mileage may vary with some of these; some don't mean to have a funny shtick but I just find them funny personally

Spinal tap

Them being ska punk makes it an easy pick, but Russkaja has great covers and original songs.

Andrew WK

Until you listen harder.

Estradasphere and Ween pop to mind

Somebody already recommended Primus so I have to come up with backup. And that is:

• Nuclear Power Trio
• Carnival in Coal
• Igorrr

Ween, Dead Milkmen, Gwar, Nomeansno, Hansen Brothers, Pink n Brown, Jesus Lizard, Moistboyz, Stormtroopers of Death.

Devin Townsend

How silly are you looking for? It doesn't get sillier than We Ran Out Of CD Space by PsychoStick... or anything else by psychostick. But there's also Ninja Sex Party, Wolves of Glendale, First of October (listen to Ravioli).

While not outright comedy, there's a humor to Falling for Me by Parker the Bandit and It's Okay to Punch Nazis by Cheap Perfume

Maybe Beck? Que’ Onda Guero always makes me giggle.

And, a bit of a different genre but Father John Misty’s songs are sarcastic and often nonsensical. They sound all romantic and dreamy but the lyrics don’t always match the vibe.

Angus McSix (formerly Angus McFife of Gloryhammer) is a hoot.

Kendall Street Company

Macklemore

Here's one you never heard of - Gung Ho by Shaka Ponk

https://music.youtube.com/watch?v=eahh8Xb41u8&si=_-tKGTX4u2iaoqiL

I only know a couple singles, but I get the sense Primus is pretty wacky