Maximum spped in electrified territory is 80 MPH for both M-7/ M-3 equipment, and DE/DMs with C-3s.
In Non electrified territory, DE/ DM's maximum speed is 65MPH, however, just like in electrified territories, there are permanent speed restrictions in place that do not allow the speeds mentioned above. Some branches have a lower MAS than others because of curves, interlocking speed limits, or track conditions that warrant a lessor speed.
As for the highest speed that the equipment is capable of reaching, (off the LIRR if they ever had a chance to)
M-7's are suppose to be rated at a Maximum speed of 120MPH, and I believe that the M-3's are 100+, although I wouldn't want to do more than 80 with them!!
DE/DMs were rated at 110MPH max, C-3's I believe are just 100MPH max. In any case, you will never see those speeds on the LIRR.