Most likely it’s because you have the username and password. Permission pleeeeze? I love pseudo-1920s stuff if it’s well done. 
I’ve gotten fond of space age bachelor pad music; currently playing is Enoch Light’s “Hernando’s Hideaway.”
If you want something that’s not really weird, but definitely offbeat, try Moondog.
Warning! There’s weird, and then there’s weird. This stuff is really weird.
The Residents: Anything and everything. Not only have they been around for thirty years without revealing their identities (they wear disguises when they play), this strange group has created some of the most original and the most moving weird music you will ever hear. Absolutely essential!
Hafler Trio: Despite the name, its only one guy. Great stuff, but hard to find.
Lucisferrato: This Russian group will give you nightmares. Hard to find, but worth the effort.
Coil: Jon Balance’s death a couple of years ago ended this incredible art project. Music to Play in the Dark vols 1 and 2, are highly recommended.
Cold Meat Industry: This Swedish label has a stunning array of talented, and very weird artists. My current favorite: Beyond Sensory Experience.
Nurse With Wound: Steve Stapleton’s work is nothing short of amazing. Dozens of CD’s, each weirder than the last.
Current 93: This band’s Black Ships Ate the Sky is hands down the best CD I’ve heard this year. Maybe the best in several years.
Inade: Weird awesome European music.
I could name dozens more. There is some just phenomenal music coming out of Europe right now.
Define weird.
A couple I doubt anyone would disagree were weird, though:
Stovokor - Klingon Death Metal
Voltaire - A lot of his stuff isn’t weird at all, but then he has things like Dead Girls (about necrophilia), Future Ex-Girlfriend (a love song about a girl he knows he’s going to dump soon after getting together with her), or the entire Banned on Vulcan album (particularly Sexy Data Tango - which is…a series of Star Trek themed double entendres about Data.
Also I love William Shatner’s singing…that’s probably weird to some.
Really?
I have a few of his tracks. I have a collection of the worst Beatles covers I could find (don’t ask, but I am curious about that I am the Walrus track) and that’s pretty weird, but I love it only in the sense that I love Plan 9 From Outer Space.
I really like The Fiery Furnaces’ Rehearsing My choir. It’s a tribute to the band’s grandma featuring the frog-voiced woman croaking her reminiscences through every track with no regard for anything approaching conventional song structure.
But what qualifies as weird is indeed an open question.
And imagine my shock that a guy calling himself Fast ‘n’ Bulbous would mention Captain Beefheart. And I love the XTC cover of Ella Guru by the way.
Bulbous, also tapered.
Polyphonic Spree. Look them up and be sitting down when you do.
Indie pop is weird?
Indie *anything * is weird! 
It’s almost scary how many of the musicians already mentioned that I listen to. Several of them have come up on my iPod in just the last hour.
I got hooked on her music when I watched Home of the Brave with a friend of mine. And I’ve seen her live a few times, but they were always smaller sorts of concerts. Were you a fan before or after the movie? I really wish I’d seen that tour in person.
Vaguely similar is Blue Man Group. They’re known for the live performances, but they’ve released some music that stands on its own, too. Lots of non-traditional instruments. (Home Depot is a music store, who knew?) Much more rhythmic than Anderson; I usually describe them as techno-tribal.
I used to have a tape copy of their first two albums, good stuff; Sussudio in the style of Runaround Sue, Jump a la Summertime Blues. When something happened to the tape, I asked the guy who made it for me if he still had the albums. He’d sold them for a nickel each. Haven’t heard their take on Celine Dion, but I’ll try to track it down.
Definite Bobs fan here, since Janie Bob was still with them (barely missed the Gunnar Bob days).
See if you can find anything by DaVinci’s Notebook. Title of the Song is a brilliant take on the whole boy band phenomenon.
There’s a great documentary about Theremin from a few years ago. I saw a screening of it ith the director there to answer questions, and a five-piece theremin band playing. A little theremin goes a long way. I got to try one. It’s harder than it looks.
Now we’re talking; Uncle Bonsai were great. They should have made it bigger than they did, although I wasn’t much help on that score, I only discovered them after they’d broken up. I’ve been to a couple of the reunion shows, though. Be sure to check out Andrew’s other projects, Mel Cooleys and Electric Bonsai Band. You can’t get the complete Doug songs without them.
I have some friends who were big Negativland fans, maybe still are. They got their copies of U2 the day it was released and it wasn’t very much later that it was taken off sale because of a lawsuit.
When CDs were starting to displace vinyl, my friends and I used to wonder if some recordings would become unknown or if everything would eventually be rereleased. This album figured prominently in such debates. And it was.
To add a few new ones:
Christine Lavin, songs about dancing amoebae and whether Pluto is a planet or not (written back when we all thought it was).
Moxy Früvous, kind of a canadian They Might Be Giants.
Saturday Morning: Cartoons Greatest Hits, a compilation album of alternative bands covering old cartoon theme songs. The Reverend Horton Heat turns the Jonny Quest Theme into scorched-earth rockabilly/surf, and Liz Phair can sing “Fleegle, Bingo, Drooper and Snork” and make it sound really sexy.
Shonen Knife, a cross between Hello Kitty and the Ramones.
Wir Sind Helden, german (the name means “We Are Heroes”), I don’t know what they’re saying, but it rocks.
Ooh, The Ballad of Bilbo Baggins (Leonard Nimoy) just came on the shuffle play…
Shonen Knife…weird?
I grant, they have a surprisingly broad pallet of songs, but weird?
Riding on the rocket I wanna go to Pluto
Space foods are marshmallows, asparagus, ice cream, ooh
Blue eyed kitty cat said, “Please let me go with you”
I’d say that’s at least slightly odd.
I dunno, it’s just CUTE, not particularly strange.
Then again, 90% of what I listen to has stuff like that.
The Langley Schools Music Project:
It’s a collection of covers of rock songs done in 1976 and 1977 at end-of-school concerts at some rural British Columbia junior high schools. The music director for the schools was a hippie ex-musician who didn’t know exactly what he was supposed to teach his students to sing. The CD is collected from the two albums he put together (as the typical sort of school music album that no one but parents will buy), but the albums were mostly forgotten till they were discovered in a junk shop more than twenty years later. Read the blurbs on the webpage from a number of interesting people. The website is part of something called “Songs in the Key of Z” that collects strange music.
Also, read the reviews on the Amazon webpage for this album (which is subtitled “Innocence and Despair”).
I did try to restrain myself, but
[one trick pony] dammit, The Incredible String Band is magnificently weird[/otp]
YouTube example
I live my life with “turn that shit off” ringing in my ears. 
If the two CDs are Made in USA and Happy End of the World, you should definitely give them a listen. Those two are my favorites. Also excellent was The Sound of Music. Pizzicato Five’s sound is hard to categorize – lounge, bossa nova, '60s hipster are all influences, but the synthesis of these styles is uniquely theirs.
And I’m gonna toss another vote on the pile for Shonen Knife being weird. How many other pop bands do you know that would have two versions of Tortoise Brand Pot Scrubbing Cleaner’s Theme on one album, along with a song the refrain of which screams out “SHE’S AN INSECT COLLECTOR!”? Fun group, though.
The Morrigan are a mixture of progressive rock and folk. Imagine the offspring of Peter Gabriel era Genesis and Fairport Convention.
Almost forgot—I’ve got a few tracks from Doctor Steel. Kinda hard to describe…make that REALLY hard to describe. But it’s sung, in character, by a Mad Scientist. With such themes as building a robot army, nuking the world, or going mad after being fired from a toy factory then attacking it with an army of knife and flamethrower-wielding dolls.
Cool guy.