Blurred lines between right and wrong
The Oresteia acts as a warning to those who believed in an absolutely binary of Good vs. Evil. In the times of Aeschylus, the Greeks had defeated the Persians and this should've been seen as an act of triumph over the barbarian that existed on both sides, rather than the Good vs. Evil theme. In the works of Aeschylus, we see a sense of moral ambiguity, and the right is not completely distinct from the wrong. This complexity of the delineation of moral ideas acts as a design that guides the entire work of art. The characters are not "bad," but are rather unfortunate to have fallen hostage to misfortune. Perhaps this is a way of conveying the hard truth of life and showing how unfair life really is.
Futility of crime
The legacy of the House of Atreus continues to affect generations of the house who are caught in a vicious cycle of blood crimes. Aeschylus sends a moral message that crime can only beget crime, leading to inevitable doom. This might even imply the greater idea of futility of war and bloodshed as symbolized by the House of Atticus.
The inherent conflict between the old order and the new
The Erinyes represent the ancient, primitive laws which demand blood vengeance, while Apollo, and particularly Athena, represent the new order of reason and a more forgiving form of religion. There is a clear theme of the clash between the old order and the new and the inevitable fall of the old order and the rise of the new.
The complex nature of inheritance
Orestes is destined to retaliate for his father's murder. While he never takes a step back, he also doesn't delight in what he has to do. Clytamnestra had sent him away to eliminate the potential threat of his resistance. Aeschylus therefore shows the complex nature of inheritance wherein while Orestes cannot choose his birthright or the sense of duty that comes with it, he does choose the way he acts on this sense of duty. This ambiguity leads to a complex nature of inheritance that has been woven in the tale.
