Answer:
The river leading to the underworld that the boatman Charon rides his ferry along. The gods swore oaths on the Styx because the minor river goddess styx (every river and tree etc had their own god/goddess) had the power to make them keep their word.
also
In Greek mythology, river of Hades that the souls of the dead had to cross on their journey from the realm of the living. It was a sacred river, and by its name even the gods took their most solemn oaths. The river was personified as a nymph, daughter of Oceanus and Tethys and mother of Nike.