As in most drama, the characters of Medea are mainly defined through their actions. Medea's vengeful nature is revealed in her plotting and murdering. Jason's ultimate disloyalty is shown when he kicks his wife to the curb for fresh young virgin. Creon shows that he's an old softy when he lets Medea stay another day on account of her sons. And, of course, there's the dutiful Nurse, whose sense of loyalty overrides her own morality as she stays true to her mistress, Medea, throughout bloody events of the play.
Social status plays an important role in defining the characters in Medea. First, there's the Nurse and the Tutor who, being slaves, are the lowest on the totem pole. They have to just do what they're told no matter what.
Medea is a foreigner which makes her have the next lowest status. Even though she is of royal blood, it's of an Asian kingdom, so that doesn't count with the Greeks. And of course, she's a woman, which doesn't give her a lot of power in Ancient Greece. Medea's low social status adds fuel to her anger, and helps to fan the flames of revenge.
Let's also consider Jason's social status. He's a legendary hero, so he's got a certain amount of clout. Also, though, he's a man of royal blood that's never had the chance to rule. This undoubtedly fuels his desire to marry Creon's daughter, which of course is what starts all this terrible business to begin with.
You can learn a lot about the characters in Medea by the way they treat their family. Both Jason and Medea express love for their sons, showing that each of them has a softer side. Of course, this is kind of negated when Jason deserts them and Medea kills them. The true family man of the play seems to be Creon, who dies when he throws himself on the flaming corpse of his beloved daughter.