In addition to the Doom room and the Wolfenstein room, I have also heard that there is a secret level as a homage to id Software's game Quake.
Where can I find this level and what do I need to do in order to access it?
To find the Quake level, you will need to search the Wasted Garage for three hidden buttons. It is recommended not to attempt to find these buttons while completing the mission to collect parts for your buggy, due to the number of enemies in the level.
The buttons do not have an on screen prompt, but you will know when they've been activated as they make a Quake-like sound when pressed.
Here is a youtube video detailing where to find these buttons and the entrance to the hidden room: