Who does that leave onstage? Well, Athena for one, and the jury of Athenians… but also the Furies. And boy are they ticked off.
Immediately, the Furies start dancing and singing: the content of their song expresses their total rage at what has happened. They interpret this as the effort of the younger gods to overturn everything that the older generations of gods (including themselves) stand for. They threaten to poison the crops of the Athenians, and generally bring havoc on the land.
In response, Athena reminds them that they submitted to the judgment willingly, and that the trial was fair. She promises to give the Furies a home in Athens, where they will be honored as divinities. But, in return, they must promise not to destroy the Athenians' crops, and so on.
But the Furies don't listen; they just repeat the same complaints and threats from before.
Athena then repeats more or less the same message; this time, however, she weaves into it the fact that she is the only one of the gods who has the keys to Zeus's lightning stash.
Although she doesn't spell it out, it's clear that she is warning the Furies that she could strike them with lightning if they get out of line.
But the Furies don't listen; they just keep grousing.
Then Athena repeats her promise to make the Furies goddesses in Athens. She is careful to speak respectfully towards them, honoring them for being older.
But she is also firm: she tells them that, if they do stay in Athens, they can't stir up any trouble between the citizens. There's already war with other cities, no need to start it within the city.
The Furies keep complaining.
Then Athena comes to the point. She tells the Furies that she will keep making them good offers over and over again. They are free to take her up on them or reject them, as they see fit. But, for the very same reason that they have received these offers, they can't make any trouble for the Athenians.
Then the Furies say, "Wait, tell us again. What sort of honors are you promising us?"
After some back and forth, Athena explains that she wants them to change their job. She wants them now to be goddesses responsible for bringing good things to good people.
The Furies say—through singing—that they accept this. Then, Athena, also singing, says that this is good. She points out that the Furies will still bring harm to people who are bad (or whose ancestors did bad things).
Then the Furies sing again; they say that they will not destroy Athens, and pray for good things to happen to the city.
Athena sings again, basically repeating what she just said: that the Furies will still punish evildoers, but they will also reward people who do good.
The Furies keep singing too; they pray for good things to happen to Athens.
Things keep going back and forth like this for a while. Strikingly, the Furies even pray for an end to revenge-killings among the citizens, because it is destructive of civic order.
After a bit more of this back and forth, Athena invites the Furies to follow her to their new home. This home will be under the ground.
Athena makes a long speech about all the good stuff that is going to come about once the Furies take up their new role.
The play ends when a Chorus of Women Temple-Servants takes up Athena's theme, now in the form of prayers of welcome for the new goddesses.