The Offspring, The Beastie Boys, Van Halen w/DLR, and the B52s. Are there other bands that rock, but are often silly/goofy and funny?

Man, that's just wacky to see those bands in one sentence in reference to rocking and being silly. You're not wrong.

One of my favorites - Frank Zappa's Apostrophe / Overnight Sensation.

Bloodhound Gang, Blink 182, Sum 41, Sublime, Men Without Hats, They Might Be Giants, Tenacious D, Ugly Kid Joe, Green Jelly / Jello, The Dead Milkmen, Dee Lite, Squeeze.

Does Weird Al count? Because he is just as talented as any "serious" musician.

Also, The Presidents of the United States of America.

Queen. They’re essentially the Monty Python Team of hard rock.

System of a Down is an equal mix of the most serious and fun songs that I've ever seen.

🍌🍌🍌🍌🧱🍌🧱, 🧱🥧

Primus sucks

WEEN

Hands down my favorite band ever (though, Faith No More could claim that spot depending on my mood.). Put their entire library on shuffle and you'd think you're listening to multiple bands. Extremely talented musicians, quirky songs, fun compositions, and a variety and uniqueness rarely found coming from one band.

All hail the mighty Boognish!

They Might Be Giants

Strapping Young Lad / anything Devin Townsend

Zimmer's Hole

Dethklok

Mindless Self Indulgence

Punky Bruster's Cooked On Phonics

Das Racist

DANGERDOOM

Handsome Boy Modeling School

The Lonely Island

MC Paul Barman

Big Dumb Face

Mr. Bungle

Lovage

Man... Or Astro Man?

Electric Six

Ween

Dead Kennedys / anything Jello Biafra

Mean Jeans

Flight of the Conchords

Presidents of the United States of America

Reverend Horton Heat

The Unicorns

EDIT: The Chats

EDIT 2: Atom and His Package

EDIT 4: Voodoo Glow Skulls

Richard Cheese & Lounge Against the Machine

Chromeo

Only Some Funny Songs:

Mountain Goats

Tom Waits

EDIT 3: Beck

EDIT 5: Flaming Lips

A League of Their Own:

GWAR

Most Importantly:

Weird Al Yankovic, because he fucking rocks god damn it. ___

Just rock or is metal allowed? Cus if so:

Ghost (Ghost B.C. in the UK) is very silly. Guys dressed in corpsepaint clergy, sounding like a hodgepodge of 70's/80's hits you missed. They got lore too, which is appropriately silly.
Electric Callboy is silly. They are... Like, deathcore mixed with whatever they feel like for that song. We Got the Moves is deathcore with a bit of hard bass, for example. And it's a song about partying. Pump It is about going to the gym. Spaceman is about a guy going to space and rapping in german. Honestly one of my favourite bands.
Wind Rose is silly as hell. Bearded guys, singing about dwarf stuff. They covered Diggy Diggy Hole and blew up, and props to them because their version is a banger, but they got good original stuff too which is sadly overlooked because Diggy Diggy Hole was just that good.
Powerwolf is another one, similar to Ghost. They're vampiric werewolves? And their songs are all in-keeping with that theme. Power metal though, unlike Ghost.
Austrian Death Machine is also silly. Voice actors emulating Arnold while the vocalist growls about lifting weights, the cookie monster, jingle bells, getting to the choppah, etc. The vocalist's history has kind of soured the band for me though.
Gnome is underrated. Their songs are simplistic as hell, and none of them are virtuosos. But their songs go hard. Wenceslas is great, Ambrosius as well. Edit: writing this gave me an earworm and went down Gnome's songs. Their bassist is a goddamn genius. Simple licks that sound great, and they got weird time sig changes here and there that tickle my brain in the best ways. I can't figure out if they are actual time sig changes or just weird changes, and I love that.

Barenaked ladies

Tenacious D

Electric Six

I think I saw someone mention them, but I can't find them now. They're pretty silly, but also their songs are unironically fun to listen to as well.

I didn't see this one yet....

Weezer

Bowling for Soup

GWAR

Butthole surfers

They Might Be Giants?

System of a Down - Cigaro

Individuals and groups in English:

Beck
Green Day
Silverchair
Busta Rhymes
Missy Elliot
Eminem & D-12
Snoop Dogg
Immortal Technique
Red Hot Chili Peppers, especially Flea
Black Sabbath/Ozzy Osbourne
The Beatles
Daft Punk
Brad Paisley
Pitbull

Spanish:

Residente & Calle 13
Los Van Van
Tromboranga
Kola Loka
Charanga Habanera

Pirate metal is fun and silly.

Adam and the ants

Reel big fish

The dead milkmen

Talking heads

Devo

Mr Bungle. The singer from faith no more. Apparently he liked hiding his turds in ventilation ducs in the hotels while he was on tour. Also made fun of the other lead singer of RHCP.

Lagwagon, nofx

Devo

Super Furry Animals

Weird Al

Frank Zappa

Devo

Nobody mentioned steel panther yet. Quality stuff

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

Any time drummer Tré Cool takes the stage at a Green Day show, you’re in for a treat. Dominated Love Slave is his signature, but there’s also Like a Rat Does Cheese which is unreleased and All By Myself closes Dookie.

There is a lot of hip hop that fits this idea of great music with wacky lyrics.

Megan thee stallion, cardi b, and the like sing some raunchy songs.

Bbno$, yung gravy, lil dicky, flynt flossy and the entire turquoise jeep records collection of artists are humor-forward

Then theres czarface which has made many albums all about comic book characters.

Svinkels, Stupeflip, MC Frontalot

Vulfpeck

Steel Panther

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

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.

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.

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.

Devin Townsend

Nerf Herder

No More Kings

Sparks. Best. Band. Ever.

Andrew WK

Until you listen harder.

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

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

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

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

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

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

Nuclear Power Trio
Carnival in Coal
Igorrr

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

Spinal tap

Macklemore

The Aquabats

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.

Estradasphere and Ween pop to mind

spose

THE TUBES

The Tubes

White Punks On Dope

Try Engerica

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

Igorrr is its own music genre

https://www.youtube.com/watch?v=WFxDOV6IwHk

(Not really, it's a blend of metal and breakcore)

In my search for artists like the Beastie Boys I came across Joey Valence & Brae and I'm loving their music.

Freak Kitchen, and their front man, now solo artist, Matthias IA Eklundh.

Southern Culture On The Skids https://youtu.be/T9NLgyEFzOo?si=w0c80_Pv1FL1qALV

Steel Panther, before they jumped the shark.

Mindless Self Indulgence.

Southern Culture on the Skids

The Reverend Horton Heat

Camper Van Beethoven

The lonely island. Although they're always silly and funny, not just often.

Alestorm.

Does music that is unintentionally funny count? Like how you laugh at a bad B-movie?

Because if so...

Rod Stewart.

Captain Sensible. He was the guitarist for the punk band The Damned, but had a #1 hit in the UK with "Happy Talk", a song from the 1949 musical South Pacific.

I second most of these other recommendations, but since I haven't seen them said yet, The Magnetic Fields. Somehow manages to be funny while also being very geniune and touching, which I think is kind of what I look for in a band.