I’m not talking about bad covers here, mind, just ones that are, well, odd. Like the hip-hop mix of “If I Were a Rich Man” I just heard.
While some people would call it bad, I’ll nominate the Scissor Sister’s cover of Comfortably Numb, with it’s disco tempo and falsetto vocals, as odd. Good, but odd.
Scissor Sisters’
danged misplaced punctuation.
I was going to mention the Comfortably Numb cover, too. I think it’s infinitely better than the original (which i think sucks), but it is very odd.
A third on Scissor Sisters and “Comfortably Numb”. Also, there’s the Le Tigre cover of “I’m So Excited” by the Pointer Sisters. It’s pretty close to the original, actually, but there are enough differences to make you sit up and take notice.
Was that “If I Were a Rich GIRL”? If so, that’s the new single by No Doubt singer Gwen Stefani, with female rapper Eve, and she just “borrows” the chorus.
Some of my all-time favorite offbeat covers:
“Common People” by William Shatner and Joe Jackson (awe-inspiring Pulp cover)
“Boyz In Da Hood” by Dynamite Hack (mellow rock Eazy E cover)
“Gin and Juice” by the Gourds (bluegrass-style Snoop Dogg cover)
The New Morty Show, one of those swing bands that popped up in the late '90s, did a few big band swing covers of '80s rockers: “Unskinny Bop” by Poison, “Enter Sandman” by Metallica, and “Rebel Yell/White Wedding” by Billy Idol.
I always love covers by ska bands. Reel Big Fish (“Take On Me”), Save Ferris (“Come On Eileen”), and Less Than Jake (“I Think I Love You,” “Walking On Sunshine”) all did some terrific cover songs, but any ska band will have a few fun covers in their repitoire.
Also, I completely forgot about Tori Amos. Ever hear the album “Strange Little Girls”? All covers, and all completely different from the originals. Her cover of Eminem’s “Bonnie and Clyde '97” is a particular favorite of mine. It’s chilling. Also Slayer’s “Raining Blood”, the Boomtown Rats’ “I Don’t Like Mondays”, and 10cc’s “I’m Not In Love”.
Also, there’s a country/swing/honky-tonk band in Missoula called Cash For Junkers, and they do a killer cover of “You Shook Me All Night Long”. 
That’s the song but might not be the artists, someone called Tara also has a cover.
Sandra Bernhardt did a song called “Maniac Superstar,” a mix of Hendrix’s “Maniac” with “I Don’t Know How to Love Him” from Jesus Christ Superstar. Strange and good.
Well, my favourite has alway been the Dickies’ "Knights In White Satin. I dunno, if there was ever a song that needed a punk remake it was “Knights In White Satin”.
Jim Thirwell and Lydia Lunch did and amazing version of “Why Don’t We Do It In The Road”. I don’t know if you can call it strange…it was really what the song should have sounded like to begin with.
Tori also did haunting versions of the Cure’s “Lovesong” and Nirvana’s “Smells Like Teen Spirit.”
Hey, that Cash For Junkers sounds like a band I would enjoy! I don’t suppose you like Bob Wills, Asleep At the Wheel, or Lyle Lovett’s big band stuff?
I’ve mentioned this before: Lol Coxhill’s gloriously bizarre version of I Am the Walrus trumps everything else when it comes to strangeness.
Not even close. Cornershop and their sitar and trip hop Punjabi version of ‘Norwegian Wood’.
You betcha. Especially Bob Wills (and Cash for Junkers do quite a few of his tunes). Also the Old 97’s; sounds like you’d dig ‘em. Heck, I could even get you copies of Cash for Junkers’ two albums, if you’re so inclined. E-mail me if you’re interested. Although the AC/DC cover isn’t on either of them. 
Beatles songs on a carillon. It’s. Just. So. Wrong. It sounds almost dead.
Then it gets to the line "Michelle, ma belle. . . " and as my ears bleed, I wonder if they did it all for the pun. It’s a City-owned carillon, so maybe yes, maybe no, depending on which employees were involved.
I’ll see your Cornershop and Lol Coxhill and raise you both The Residents’ cover of Elvis’s “Heartbreak Hotel” as well as the whole rest of the “King and Eye” album that were all Elvis covers). Hear a sample at Allmusic.com.
“Green Haze” by Elvis Hitler. The music is a pretty much note-for-note rendition of “Purple Haze,” but the singer inserts the lyrics from the theme from “Green Acres”:
Green Acres is the place to be… farm livin’ is the life for me…
My favorite is Sonic Youth’s cover of the Carpenters’ “Superstar.” If anything, it’s closer to the original spirit of the lyrics - it sounds like a half-speed, smacked-out suicide anthem moreso than a happy, uptempo, celebratory song like the original.
I’m partial to Me First and the Gimmee Gimmees doing *Over the Rainbow * or Phantom of the Opera, but *Stand by Your Man * is just odd in punk.
Pretty much anything by the Residents is going to be a freaky, freaky song. On my copy of Third Reich and Roll are covers of the Stones’ “Satisfaction” and the Beatles’ “A Day In The Life.” Weird.
I’ve got a couple weird/novelty records that include a Gregorian chant version of “Smells Like Teen Spirit” and classical rearrangements of “White Rabbit” and “Born To Be Wild.”