"κλύεθ' οἷα λέγει κἀπιβοᾶται / Θέμιν εὐκταίαω Ζῆνά θ', ὃς ὅρκων / θωητοῖς τμίασ νενόμισται; / οὐκ ἔστιν ὅπως ἔω τινι μικρῶι / δέσποινα χόλον καταπαυσει" (Mήδεια lines 169-172, spoken by the Nurse)The Nurse (Τροφός), adding emphasis to the oath, asks the Chorus if they heard it. Mastronarde mentions that there was a legal nature to calling particularly on Zeus and Themis.
Although there is certainly a legal nature, law in Ancient Greece was tied directly with religion. Not only could people bring the charge of impiety or atheism (e.g. Socrates), but there were religious ceremonies tied into the legal proceedings themselves (see commentary on Aeschylus' Eumenides. There may even be enough material in Hugh Lloyd-Jones' translation). At the same time, Μήδεια is talking about a legal oath and a religious one, and the strength of this oath seems to be important. Unfortunately both the scholarship and my knowledge of the complexities of oaths and Greek religion is lacking. I have looked, but little is as in-depth or satisfying as it should be.
"ΖEUS ΣΩΘΗΡ ΤΡΙΤΟΣ and Some Triads in Aechylus' Oresteia"(JSTOR) is Peter Burian's amazing article about oaths-- or more libations-- in the Oresteia. I highly recommend the article. At banquets, so far as I can tell, three libations were poured: one for the Olympians, one for the cthonic gods (i.e. the old, earthier, and darker gods like Night and Persephone), and the last to Zeus the Savior. There are a lot of interesting implications to this throughout the Oresteia. I almost wrote my thesis on the Zeus cult in the Oresteia, but too much of the scholarship was in German so I couldn't pull it off.
- Cthonic gods comes from the Greek word χθών meaning earth. They are gods that have to do with the earth (or under the earth) such as Hades and Persephone, as well as the "older," primordial gods like Night. More on cthonic cults and gods at some other time.