The Who were kinda silly (eg: Boris the Spider) in their early years.

Nobody mentioned steel panther yet. Quality stuff

Ween.

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.

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.

Electric Callboy are very silly and produce excellent videos.

JBO, if you understand German.

fine young cannibals, wall of voodoo/stan ridgeway.

Sparks. Best. Band. Ever.

if ska counts, reel big fish

Estradasphere and Ween pop to mind

The Aquabats

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.

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

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

Macklemore

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

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

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

• Nuclear Power Trio
• Carnival in Coal
• Igorrr

Kendall Street Company

Spinal tap

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

Devin Townsend

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

Thank You Scientist are seriously talented musicians who make very complex music, but don't take themselves seriously and have fun with their performances.

Future Idiots.

Patent Pending.

Andrew WK

Until you listen harder.

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