This is a really broad question, but I can at least tell you that oaths like "by Castor" ((e)castor) "by Pollux" ((ede)pol) and "by Hercules" ((me)hercle) are commonly sprinkled through Roman comedy . It's difficult to say whether they were used by ordinary people, since Plautus and Terence (3rd-2nd cent. BCE) are the only places where they're found in direct speech. JB Hoffman's Lateinische Umgangsprache (1950) has a pretty thorough look at these expressions, if you read German or Italian (trans. Licinia Ricottilli 1980).

It's accepted that Alexander the Great had massive admiration for the exploits of Hercules, often trying to follow his footsteps or become like him (Including allowing a mistaken translation at the Shrine of Siwah making Alex out to be the son of Ammon, or Zeus, like Hercules) Being in the late 4th century BC (330's-320's) this seems sufficiently ancient. Alexander also made his fatal mistake of crossing the gedrosian desert because he believed only Hercules had done it first. (Plutarch) At the siege of Tyre, Alexander had a vision/dream of Hercules on the walls of the island fortress, beckoning him, among other dreams. He took this as both a sign and a challenge, it seems, again not wanting to fail his image of Hercules. Sources: Arrian - The Campaigns of Alexander Plutarch - The Age of Alexander