After a six year hiatus, I’m requesting again the strange and offbeat. The requirements:
Some new bands/performers that I’ve found since then:
Ex-Girl
Extra Action Marching Band
Exuma
Jay Munly
OOIOO
R.I.P. by Zombie Ghost Train.
Dead Man’s Bones - In The Room Where You Sleep
Bruce Peninsula - As Long As I Live
Bel Canto - Spiderdust
Aisha Kandisha’s Jarring Effects - Muey A Muey
Diamanda Galas / John Paul Jones - Sporting Life
Melinda Miel - The law of the dream
Antony And The Johnsons - Cripple And The Starfish
Boiled in Lead - The Microorganism
Control Machete - SI SEÑOR
Scott Walker - Jackie
Lee Morse - T’Ain’t No Sin To Take Off Your Skin
I was at work when I posted the OP. Here’s the same list, with YouTube links:
eX-Girl :: Hettakorii No Ottokotou
Extra Action Marching Band :: Unknown
Exuma :: Mama Loi, Papa Loi
Jay Munly :: Cat
OOIOO :: Asozan
Akiko Yano - Rose Garden
Takako Minekawa - Plash
butter 08 - Butterfucker
Foetus - Slung
Steroid Maximus - Quilombo
DIAMANDA GALAS & JOHN PAUL JONES - HEX
Ingrid Karklins - Leatherwing Bat
ETHYL MEATPLOW - QUEENIE
Ragga and the jack magic orchestra - Where are they now
Johnny Dowd - No Woman’s Flesh
Danielle Dax - PARIAH
Death Grips - Gullitione You might think he loves you for your money but I know what he really loves you for it’s your brand new leopard skin pillbox hat
King Krule - Rock Bottom Easy Easy
Death Grips is pretty much unclassifiable, you have to listen to their songs and even then it’s hard to put them in a box.
King Krule is more mainstream, wikipedia pegging him as " punk jazz, hip hop, darkwave, and trip hop."
Hazmat Modine
There’s also Ryoji Ikeda, he seems to one of the very few artists to use very high and very low registers together, and has a really modern, clean and sharp sound to him.
Ninja’d by lissener on Danielle Dax, awesomely weird. Sharp intelligent lyrics wrapped in Indian/New Wave fusion 30 years ahead of its time.
Hedningarna, Swedish electronic-folk fusion with lots of yodeling and fuzzboxed-didgeridoo.
Weebl of badger badger fame. His live show is awesome 
The Dickies, with their iconic penis puppet.
I wasn’t around six years ago (or maybe I just missed that request) but back then I would have listed the following (already old) artists:
Spike Jones: Spiked (anthology?)
Twang Bang: Nothing Quite as Wholesome as a Fish
Tony Mason (used to have a website full of oddball stuff). A Bad Idea and Barney Must Die are especially good.
–G!
When you told Bruce Lee
You could kick his ass
It was a bad idea
It was a bad idea
…–Tony Mason
…A Bad Idea
…No Smurfing Allowed
Noises of Russia -Spirit
More examples of the absolutely incredible and wonderfully bizarre underground Russian music scene:
I see Einsturzende Neubauten and Birthday Party were mentioned in the other thread, Foetus in this one. The other bands that I like that I get similar looks for:
Young Gods (that’s an acoustic session, the original is …harder)’
Swans (who over their/his (Michael Gira) career were capable of this and this and this)
Then there’s stuff like
Yat-Kha…
As far as I’m concerned, The Residents are the primordial root of the cause.
Hallucinogen - Gamma Goblins
Couch Flambeau - Vipers - I wanted to lync Wot a Caper but Youtube doesn’t have it
Dengue Fever - Seeing Hands - Cambodian pop
Future of the Left - Robocop 4 - Fuck Off Robocop The guys who used to be McLusky doing their warped thing
Gabba - Mama Mia - An Abba/Ramones crossover
T. Valentine - Hello, Lucile are you a lesbian? I swear this guy has some sort of problems.
Yet more:
and a rare Christmas in July Special:
Worth mentioning Australian masked marvels TISM[short fror This is Serious Mum].
A good introduction is their Great Trucking Songs of the Renaissance double album, or their live video [title inspired by Ted Nugent’s Intensity in Ten Cities] Incontinent in Ten Continents.