I just picked up the soundtrack to Four Rooms, and this is a very quirky and admittedly acquired taste of an album.
I really can't describe what type of music this is. The band, Combustible Edison, seemingly sings gibberish lyrics over some truly unique instrumentals. They are classified as a "lounge" band.
Interesting note, Combustible Edison's track "Vertigogo" which was the opening theme to the film "Four Rooms", was ruled ineligible by the people behind the Academy Awards due to the lyrics being "not intelligible".
This is the rarely seen promo video for their song "Vertigogo".