I wouldnt call anything in my library too unusual... pretty much still all constitutes as music... that being said I tend to enjoy a large variety of more eclectic/eccentric/nostalgic music that diverges from mainstream radio.
Some notable artists:
cocorosie - "freak folk", and incorporates elements of pop, blues, opera, electronica, and hip hop.
god speed you! black emperor - Canadian post-rock, instrumental rock, experimental rock.
horse the band - 8-bit nintendo metalcore
B.A. johnston - rock acoustic/sugar pop