At the Facebook page for The Unusuals is a list of the music used.
I’ve filched that list and added links to where that music can be heard on the Internet.
If there’s audio or a video, the title will have a link. Band/artist name will be a link to a website, if available.
Note: These are all publicly-accessible links and not part of any affiliate program.
Episode 1: Pilot
“I’m Good, I’m Gone” by Lykke Li
“The Beat Is” by Channel Two
“Cobra Style” by Teddybears featuring Mad Cobra
“No Biterz” by Miss TK and The Revenge
“Bollywood” by Shawn Lee’s Ping Pong Orchestra
“Murder” by Enemy Voices
Episode 4: Crime Slut
“Boom Shot Dis” by Kully B & Gussy G
“Believe It (Over You)” by Vallejo
“Encore Une Nuit (Just Another Night)” by Chapeaumelon
“Metal Heart” (2008 version) by Cat Power (from Jukebox)
Music of episode six haven’t been listed yet.