R. S. P. Beekes has suggested a Pre-Greek proto-form *-kay-an-. In contrast, Michael Janda has reminded the scientific community of an earlier comparison of the Vedic dragon Vṛtra's attribute āśáyāna- "lying on " and Greek Ὠκεανός (Ōkeanós), which he sees as phonetical equivalents of each other, both stemming from a Proto-Indo-European (PIE) root *ō-kei-ṃno- "lying on", related to Greek κεῖσθαι (keîsthai "to lie"). Janda furthermore points to early depictions of Okeanos with a snake's body, which seem to confirm the mythological parallel with the Vedic dragon Vṛtra.
Another parallel naming can be found in Greek ποταμός (potamós "broad body of water") and Old English fæðm "embrace, envelopment, fathom" which is notably attested in the Old English poem Helena (v. 765) as dracan fæðme "embrace of the dragon" and is furthermore related (via Germanic *faþma "spreading, embrace") to Old Norse Faðmir or Fáfnir the well-known name of a dragon in the 13th century Völsunga saga; all three words derive from PIE *poth2mos "spreading, expansion" and thus bind together the Greek word for a "broad river, stream" with the Germanic expressions connected to the dragon's "embrace".
According to Homer, Oceanus was the ocean-stream at the margin of the habitable world (οἰκουμένη, oikouménē), the father of everything, limiting it from the underworld and flowing around the Elysium. Hence Odysseus has to traverse it in order to arrive in the realm of the dead. In the Iliad, Hera mentions her intended journey to her foster parents, namely "Oceanus, from whom they all are sprung":
Helios rises from the deep-flowing Oceanus in the east and at the end of the day sinks back into the Oceanus in the west. Also the other stars "bathe in the stream of Ocean". Oceanus is called βαθύρροος (“deep-flowing”) and ἀψόρροος (“flowing back to itself, circular”), the latter quality being reflected in its depiction on the shield of Achilles:
In Greek mythology, this ocean-stream was personified as a Titan, the eldest son of Uranus and Gaia. Oceanus' consort is his sister Tethys, and from their union came the ocean nymphs, also referred to as the three-thousand Oceanids, and all the rivers of the world, fountains, and lakes.
In most variations of the war between the Titans and the Olympians, or Titanomachy, Oceanus, along with Prometheus and Themis, did not take the side of his fellow Titans against the Olympians, but instead withdrew from the conflict. In most variations of this myth, Oceanus also refused to side with Cronus in the latter's revolt against their father, Uranus. He is, it appears, some sort of an outlaw to the society of Gods, as he also does not – and unlike all the other river gods, his sons – take part in the convention of gods on Mount Olympus.
Besides, Oceanus appears as a representative of the archaic world that Heracles constantly threatened and bested. As such, the Suda identifies Oceanus and Tethys as the parents of the two Kerkopes, whom Heracles also bested. Heracles forced Helios to lend him his golden bowl, in order to cross the wide expanse of the Ocean on his trip to the Hesperides. When Oceanus tossed the bowl about, Heracles threatened him and stilled his waves. The journey of Heracles in the sun-bowl upon Oceanus became a favored theme among painters of Attic pottery.