This is what the Encyclopaedia Britannica says about the river:

Styx, in Greek mythology, one of the rivers of the underworld. 

The word styx literally means “shuddering” and expresses loathing of death. In Homer’s Iliad and Odyssey, the gods swear by the water of the Styx as their most binding oath. According to Hesiod’s Theogony, if a god perjured (ean pei psemata efoson orkisti oti tha pei mono tin alitheia) himself, he was rendered insensible for a year and then banished from the divine society for nine years. 

Perhaps because of its similarity to Hesiod’s description in Theogony, the Styx later was identified with the stream now called Mavronéri (Greek: “Black Water”) near Nonacris in the Aroania Mountains (near modern Sólos) in Arcadia. 

The ancients believed that the river’s water was poisonous and would dissolve any vessel containing it except one made of the hoof of a horse or an ass. There is a legend that Alexander the Great was poisoned by Styx water. In another legend, mentioned by the Roman poet Statius (1st century ad), Thetis dipped her son Achilles into the Styx to render him invulnerable; because she held him by his heel, he remained vulnerable there.