Most of the music in the game is by EnV (Envy).
His newgrounds page: http://envy.newgrounds.com/
His youtube channel: http://www.youtube.com/user/EnvyNG
His soundcloud page: https://soundcloud.com/envyofficial

Other authors include Twistex, Getsix and Goto80, which have their songs appear in some of the Micro-Hell levels.

The soundtracks are listed in the following format:
Level - Soundtrack name

I added a link for most songs, but only to versions uploaded by authors themselves on their official pages.

Asterisk (*) next to a soundtrack name means the song is included on the official Electronic Super Joy OST digital albums. You can buy the albums here:
http://electronicsuperjoy.bandcamp.com/album/electronic-super-joy-ost
http://electronicsuperjoy.bandcamp.com/album/electronic-super-joy-ost-part-ii
The albums also include Green With Me[www.newgrounds.com], which doesn't actually appear in the game.

Trailer - Shakestopper[soundcloud.com]*
Intro music - Destination[www.newgrounds.com]*
Infinite Love Mode - Vee[soundcloud.com]*

Stage 1
Welcome (intro text) - Something New[www.newgrounds.com]
Welcome - Flare[www.newgrounds.com]*
Sunlight Grooves - This Sound[www.newgrounds.com]*
Club ESJ - Revive[soundcloud.com]*
Black And White - Generic Techno[www.newgrounds.com]*
Bounce Party - Revive[soundcloud.com]*
Crushinator - Sanctuary
Drop The Beat - Shakestopper[soundcloud.com]*
Pretty In Pink - OCP[www.newgrounds.com]*
Slowdance - FireFrost[soundcloud.com]*
Everybody Loves Me - Uprise[soundcloud.com]*
The Pope - Darkas*[www.newgrounds.com]
Pope 2: Hyper-Pope - Destination[www.newgrounds.com]*
Star League - Heaven Rd. 3[www.newgrounds.com]*
Star League (end of level) - Sidechain Test[www.newgrounds.com]
Pride - RPM[soundcloud.com]*
Sudden Death - Heaven Rd. 3[www.newgrounds.com]*

Stage 2
Babylon - Darkas*[www.newgrounds.com]
Again Please! - Sanctuary
Where Are The Stairs? - FireFrost[soundcloud.com]*
They Bleed Rip-Offs - WobbleWobble[www.newgrounds.com]
Orange You Glad - Uprise[soundcloud.com]*
I Didn't Say Banana - Uprise[soundcloud.com]*
It Builds Character - Futureshock[www.newgrounds.com]*
Laserz - Valiant[soundcloud.com]*
Here Ya Go - Darkas*[www.newgrounds.com]
Evil Unicorns - Revive[soundcloud.com]*
Don't Look Down - FireFrost[soundcloud.com]*
Groove Rules - FireFrost[soundcloud.com]*
Beep Beep - Absolute Zero[www.newgrounds.com]
Big Sexy Beast - Switchblade[www.newgrounds.com]*
Stepping On Tokyo - Wakkawakka[www.newgrounds.com]

Stage 3
Welcome To Hell - Call of the Wild[www.newgrounds.com]*
Big, Red And Bouncy - Call of the Wild[www.newgrounds.com]*
I Blame Your Mother - RPM[soundcloud.com]*
Over By Christmas - Heaven Rd. 3[www.newgrounds.com]*
Frogs?! - Bestammelse[www.newgrounds.com]*
Hell Club - RPM[soundcloud.com]*
Ice Ice Baby - Vee[soundcloud.com]*
I Believe! - Imagination[www.newgrounds.com]*
I Blame My Mother - Endurance[www.newgrounds.com]*
I Still Love You - Bestammelse[www.newgrounds.com]*
Run Coward! - Jump[www.newgrounds.com]
The Wizard - Monster[www.newgrounds.com]
Grooving - OCP[www.newgrounds.com]*
Flap Your Brains Out! - Switchblade[www.newgrounds.com]*
Murder - Sanctuary
Murder (credits) - Ballad for the Lost[www.newgrounds.com]

Stage 4
A Jungle Welcome - Vee[soundcloud.com]*
Ol' Ball And Chain - Sanctuary
Emotional Mess - Absolute Zero[www.newgrounds.com]
The Rabbit Hole - Bloom[soundcloud.com]*
Totally Necessary - Grizzly[www.newgrounds.com]

Bonus Content
Watch Your Step - Valiant[soundcloud.com]*
Don't Let Go - Pearlescent[soundcloud.com]
Factory Of Pain - Flare[www.newgrounds.com]*
(DLC - Bonus Content) Trecherous Footing - Pneumatic Tokyo[soundcloud.com]
(DLC - Bonus Content) Thin Ice - Endurance[www.newgrounds.com]*

Micro-Hell
Dimensional Exploration (intro text) - Something New[www.newgrounds.com]
Dimensional Exploration - Heaven Rd. 3[www.newgrounds.com]*
Acceleration Testing - Futureshock[www.newgrounds.com]*
Chrono Anomalies - Bestammelse[www.newgrounds.com]*
Portal Laboratory - Play It[www.newgrounds.com]
Micro-Hell - Pulse[soundcloud.com] by Getsix
Arrg! Not The Butt-Laser! - Enn[soundcloud.com]
Gotta get 'em all! - Minipitt by Goto80
Now I have a machine gun, ho ho ho (part 1) - Orbit[soundcloud.com] by Twistex
Now I have a machine gun, ho ho ho (part 2) - Take Me Out[soundcloud.com]
Showdown - Absolute Zero[www.newgrounds.com]

DLC - A Hot Sticky Mess
A Pretty Awful Mess (intro text) - Something New[www.newgrounds.com]
A Pretty Awful Mess - Jump[www.newgrounds.com]
A Fine Papal Mess - Valiant[soundcloud.com]*
A Black n' White Mess - Vee[soundcloud.com]*
An Acidic Spikey Mess - Play It[www.newgrounds.com]
A Big Crumbling Mess - Futureshock[www.newgrounds.com]*
A Super Giant Mess - So Far Away[www.newgrounds.com]
A High Flying Mess - Pneumatic Tokyo[soundcloud.com]
An Evil Portal Mess - WobbleWobble[www.newgrounds.com]
A Laser Danger Mess - Uprise[soundcloud.com]*
A Sticky Icky Mess - Rokits[www.newgrounds.com]
A Big Smashy Mess - RPM[soundcloud.com]*
A Tap Dancing Mess - Bloom[soundcloud.com]*
A YOLO Snow Mess - Prime Time[www.newgrounds.com]
A Heartfelt Mess - Sanctuary
A Big Ole Mess (part 1) - Uprise[soundcloud.com]*
A Big Ole Mess (part 2) - Jump[www.newgrounds.com]
A Big Ole Mess (part 3) - Futureshock[www.newgrounds.com]*
A Big Ole Mess (part 4) - Vee[soundcloud.com]*
A Big Ole Mess (part 5) - Valiant[soundcloud.com]*