WHAT IS THE MOST UNIQUE SONG THAT YOU HAVE EVER HEARD?

no contest, The Legendary Stardust Cowboy, "Paralyzed"
https://www.youtube.com/results?search_query=paralyzed+legendary+stardust+cowboy

My Ding-a-Ling Chuck Berry

https://youtu.be/XXhsqsh1uX0

I think "strange" is a better descriptor than unique, but, I kind of find Klaus Nomi covers to be interesting,  Take a look at this version of "Just One Look":

https://www.youtube.com/watch?v=2yplwTe5IFQ

Theodora is Dozing - from the Bulgarian State Women's Choir - a really unusual tune that is just indescribably beautiful. I think David Byrne did a cover version since this was one on one of those classic Folkways World music records. All of those were just the greatest way to travel the world through a record player. 

Warren Zevon - Werewolves of London. So damn catchy too.
More seriously, anything by Laurie Anderson is 'out there'.