Overdrive armor is only used once, by Omega at the end of Xionic Madness 1, and is used for a portion of the XV fight in 1.5. Overdrive armor is believed to be available to all of Bolverk Squad, however only Omega uses it.
Personally, I think that Overdrive armor is just Omega overclocking his basic armor, amplifying its effects to a level that nears XV's.