The song above is performed by Girls Dead Monster, a fictional band inside the world of Angel Beats. The band plays an important part in the Angel Beats story, but we also get to hear them perform a number of songs. I'll be damned if they aren't a fun, upbeat band!
Yes, the music in the band is performed by two real-life musicians that can perform live, but it's not like the Girls Dead Monster band actually exists. That will only live inside the anime itself, and I doubt we'll ever hear another round of tracks from this band.
At least I can enjoy 15 tracks from Girls Dead Monster, thanks to a supplemental soundtrack release that accompanied Angel Beats. Girls Dead Monster may not be a real band, but they did get an album release. Those 15 tracks will always have a place in my iTunes library. They'll just make me sad when I hear them!
Best part about all of this? My sister came to me on her own and told me she really loved the band in Angel Beats. That's without any prodding or comment from me. Glad to know others really dig the music as well! I suggest hitting up YouTube to check out some more of their tunes.