Hebrew, Greek and Latin, not Aramaic. Latin was only used by the Roman upper classes, but Greek was the common tongue of the empire since it had been spread centuries earlier by Alexander the Great and his successors. By this time it was very commonly spoken, by everybody.
Hebrew was spoken also, e.g. Paul addressed the crowds in Hebrew in Acts 21:40. However the impression I get was that it was unusual to use this language. It seems he spoke Greek so commonly that a speech in Hebrew was unusual enough for the language to be specifically mentioned.
Also, when Jesus spoke his dying words on the cross, in Hebrew, these are transliterated because of the particular significance of them being in Hebrew. And the bystanders did not understand them, and thought he was calling for Elijah. Had Hebrew been common this confusion would surely not have happened.
From these scriptures, Hebrew seems to me to be already a language venerated and used for religious purposes, but not the everyday language of the people.