In terms of plumage and behaviour, some of the birds of paradise have to be strong contenders in any 'most unusual' list. I mean, take a look at this:
(Image source: Wikpedia (Creative Commons))
This is a male Wilson's Bird of Paradise (Cicinnurus respublica), a species that's found only on a couple of small islands off the coast of West Papua. That bizarre blue cap is actually bare skin! It's certainly eye-catching, but I find those gorgeous curled tail feathers just as fascinating. They certainly stand out in this video of a male bird, which is clearing its display floor in preparation for the song-&-dance routine used to attract a female.
Like many birds of paradise, C.respublica is a sexually dimorphic species, and the female is quite drab in comparison to the male. She comes into view about halfway through this video from Sir David Attenborough, which gives a good idea of the birds' size (they're surprisingly small). The video also shows the male's display - as Sir David says, the dance moves are poor but the costume is amazing :)