I was thinking about this question and couldnt come up with a good answer, then I realized that what I was listening to at the moment pretty much fit this description.
I cant pick a song, but the 'In the Aeroplane Over the Sea' album by Neutral Milk Hotel contains some of the weirdest songs ever. On first listen, some are almost completely unlikable, containing some bizarre and off the wall lyrics and instrumentation. On further spins you start to realize all that's going on in the songs, or how simple they really are. I cannot explain why I even like this stuff to myself, I wouldnt think I'd like it in many ways.
I found this description of the album on allmusic.com, and I really agree with it:
"Perhaps best likened to a marching band on an acid trip, Neutral Milk Hotel's second album is another quixotic sonic parade; lo-fi yet lush, impenetrable yet wholly accessible, In the Aeroplane Over the Sea is either the work of a genius or an utter crackpot, with the truth probably falling somewhere in between. ....In the Aeroplane Over the Sea is undoubtedly a major statement, but just what it's saying is anyone's guess."