The gods in classical antiquity had specific duties associated with them, but in general these duties were pretty fluid and the gods could come to be associated with many things.

The god Apollo is likely the one to be prayed to in an oratory situation, though Mercury and Minerva are also likely candidates. The prayer did not necessarily have to be directed to a specific god, instead the orator may have made a general prayer to the gods. The muses could also be invoked, as mentioned by /u/DudetheObscure. It's difficult to say for certain, but the gods and goddess mentioned above have the most explicit connection to oratory skills such as good communication and wisdom.

Source: Grafton, Anthony et al. 2013. The Classical Tradition. Cambridge, MA: Belknap Press.