There may be a lot of justice in The Odyssey, but there isn't a court of law to be found. Justice seems to be based around some divine sense of cause-and-effect: there's a certain order and balance in the universe, and bad actions (like violating guest-host laws) nets you a bad return. But this isn't the kind of justice where they put you in a cushy prison and try to rehabilitate you. It's the kind where, if you throw a footstool at a beggar, you get an arrow in your heart—and then your dad gets one in his head. Way harsh, Athene.
Questions About Justice
What kind of justice system do the gods follow? What kinds of transgressions are punishable by death?
Is there even a system at all? If the gods are subject to the same whims, grudges, desires, and pettiness as the mortals, isn't "justice" (and especially "divine justice") as inconstant and illogical as basic emotion?
Why does Athene want all the suitors to die—even the sort-of-cute-and-fuzzy ones? Is this "justice" according to the Odyssey?
How are random events like Elpenor's death justified?
Is justice in the ancient Greek system just a cover for personal vengeance? Is it fair? What does "fair" even mean in this world? Are there any instances of more civil methods of punishment and reconciliation?
Chew on This
Poseidon is unjustified in hounding Odysseus across the seas because his son Polyphemos deserved the blinding that the hero gave him.
The Odyssey shows a tentative shift away from the "you killed my son, so I'm going to kill you" kind of justice toward a "maybe it's better not to be killing each other all the time" sort of justice.