The mid-'90s had some kooky tunes, man.

My hypothesis:

Record companies had no idea that anyone like Nirvana was even out there, but there they were. Then they got Nirvana, and promoted the hell out of 'em, and made a lot of money, and then Kurt Cobain liked heroin a little too much.

So...

By the time the mid-'90s rolled around, record companies really had no idea what was going to be the next big thing, so they supported a lot of mildly-out-there bands who might fall under the big tent of "alternative."

Thus...

We had a lot of unusual bands in the era roughly from 1995 through 1998 that may have only had one hit, but it was a hell of a big hit, and that's more that most bands ever have in their careers.

I'll try to list as many as I can, in alphabetical order, along with their iconic, but mildly unusual, song that comes to mind. This list is by no means exhaustive.

Beck -- "Loser"
Bloodhound Gang -- "Fire Water Burn"
Blues Traveler -- "Runaround"
Tracy Bonham -- "Mother Mother"
Butthole Surfers -- "Pepper"
Cake -- "The Distance"
Cherry Poppin' Daddies -- "Zoot Suit Riot"
Chumbawumba -- "Tubthumping"
Daft Punk -- "Da Funk"
Eels -- "Novocaine For The Soul"
Folk Implosion -- "Natural One"
PJ Harvey -- "Down By The Water"
Harvey Danger -- "Flagpole Sitta"
Marcy Playground -- "Sex And Candy"
Mighty Mighty Bosstones -- "The Impression I Get"
Nada Surf -- "Popular"
The Presidents of the United States of America -- "Lump"
Primitive Radio Gods -- "Standing Outside A Broken Phone Booth With Money In My Hand"
Rage Against the Machine -- "Bulls On Parade"
Spacehog -- "In The Meantime"
Sneaker Pimps -- "Six Underground"
White Town -- "Your Woman"

Again, not going to be a complete list. I know I forgot a lot. Some of these artists had just the one hit, others went on to big careers. But I've always meant to put together a list like this, and it looks like a decent start.