Making a Monome using ArduinoMega256
I ordered 64 buttons (4 4x4 Button Pads) and making the PCB to hook
  it up to Arduino Mega....
  My question is how can I make my hardware emulate the actual Monome
  and use the software built for Monome?


I've never noticed the Monome before, it seems very cool! However I think it will be a bit much for an AtMega to handle. I would recomend using 1 or more atmega's to detect the button presses and toggle the LED's. Then you should use a 32bit ARM processor for the audio and communication between the AtMega(s).


  Request: Can you point me in the right direction?


You may want to look into using a Raspberry Pi as the main ARM processor. I believe they have analog audio out. 


  Question: Would it be hard to write a piece of software that that acts
  as a bridge between my hardware and Monome software?


It wouldn't be much work. However 'hard' is in the eye of the beholder! ;)

That looks like a really cool and fun project, best of luck!



It looks like using a Raspberry Pi has been discussed on monome.org: http://monome.org/community/discussion/13723/x