In Sophocles' Antigone, the playwright does not comment very much on any of these three characters and only Eurydice appears on stage or has a speaking role during the play (and it is a very brief one).
What happens in the Antigone is set in motion by the war that occurred between Polyneices and Eteocles, the sons of Oedipus and Jocasta, who were fighting over the kingship of Thebes. In the course of this war/battle, which became known as the Seven against Thebes, Polyneices and Eteocles killed each other simultaneously. A fairly detailed account of their fight can be found in Euripides' Phoenician Women, which was staged by 30 years after Sophocles' play.
Most of what Sophocles tells us about Eteocles and Polyneices can be found in Creon's comments early in the play. Creon describes Eteocles as someone who died fighting "to save our city" and who is "the best and bravest / of our spearmen" (Ian Johnston translation).
As for Polyneices, Creon describes him as someone who
...returned from exile,
eager to wipe out in all-consuming fire
his ancestral city and its native gods,
keen to seize upon his family’s blood
and lead men into slavery...
Subsequently, as readers of the play know, Antigone buried Polyneices despite Creon's decree of death for anyone who did so. Because Polyneices had marched upon Thebes, Creon regarded him as a traitor undeserving of a proper burial.
As for Eurydice, the wife of Creon, she appears very briefly at the end of the play to ask about the bad news she has heard regarding her family. When she hears what has happened to Antigone and her son Haemon, she rushes back into the palace, stabs herself to death with a sword, and curses Creon as the one responsible for Haemon's death, as well as the death of another son whose death occurred outside the action of this play.