Do you really want to use DMX or, do you just want to color change LED strips?
The reason I ask is that DMX would seem to imply a controller and perhaps remote operation to a stage. I am assuming here that you are trying to decode an incoming DMX signal and then decode it to change and/or dim your strips.
A bit more information would be appreciated and would be most useful.
There are DMX shields for Arduinos and here are a couple
http://www.arduino.cc/playground/DMX/DMXShield
http://shop.trinculosattic.com/products/the-guildenstern-arduino-dmx-shield