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.
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.
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.
Fun fact: My employer paid for my plane ticket and hotel stay that evening. It "just so happened" that I had something to do at the head office at the same time my two favorite artists were performing nearby.. sure, I had something work-related to do, but my timing was no accident.
UPDATE: Looks like Dream Theater will be in the area again in November. Sounds like it's time for a department-wide meeting, don't you think?
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.
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.
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.
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.
Thank You Scientist are seriously talented musicians who make very complex music, but don't take themselves seriously and have fun with their performances.
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.
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.