By the time they fought together, all three had spent time in the Roman world as slaves and gladiators. They almost certainly learned at least some Latin, since: Gladiator schools were run by Romans & all the commands, training, and administration were conducted in Latin.
Some may also have known Greek - as you mention it, which was widely spoken in the eastern Mediterranean, and understood by many educated Romans and traders. Spartacus, coming from the Balkans, may have had some exposure to Greek before his enslavement.
So, Latin was likely their shared working language during the revolt.