Apparently a comment has been posted (and deleted) talking about the variation in social standards for women by class: to be clear I'm aware that the ability to keep women just shut up at home was inevitably only really possible for the upper classes [as I understand it this is true of all such societies - economically unproductive women are a form of conspicuous consumption], and indeed that there were 'companions' who seem to be able to live more in a man's world and e.g. are shown debating with men in some of Plato's dialogues.

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In the plays, though, we're dealing very much with the sort of aristocratic women you'd expect to see cloistered away: daughters, wives and mothers of kings and tyrants. It's. not just depictions a no-nonsense working class women or witty courtesans. Indeed Medea highlights these limitations on a married (aristocratic) woman

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Part of it is that (and perhaps I just haven't come across it) I haven't seen the same empathic presentation either in other heavily patriachal cultures or across other divides of oppression. For instance, I haven't come across similar speeches in Greek plays from slaves setting out the injustice of slavery, even though you'd think that would be easier for playwrights to sympathise with (many of the plays are after losing the Pelopennesian War, so people must have thought death or slavery a clear and present danger)

You're right that the character of Medea says those things, but that's not the same thing as the play itself or Euripides railing against the unfairness of Athenian misogyny. Everything Medea says should be seen through the lens of what she goes onto do, which the audience would be aware of, i.e. killing Herakles' would-be bride and children, and so destroying his family line. Therefore her words are not those of a sympathetic character who is supposed to persuade the audience, instead her behaviour taints those words. Imagine a play where Hitler extolled the virtues of vegetarianism and criticised animal farming. Even if the audience could be expected the think what the character was saying was factually accurate (which isn't a given in any case), knowing their personality and how evil they are shows that the thoughts they express are similarly reprehensible.

Lysistrata is a comedy. There's a lot of debate about the extent to which Aristophanes is actually making any kind of political point or if he's just being funny. In the case of the Lysistrata, any political point is surely undermined by the ridiculousness of the women's demands: they are upset about the war and their husbands being away, and therefore they refuse to have sex until the war is over and their husbands come back. But if their husbands are away then who are they refusing to have sex with? Maybe Aristophanes is making a point about war dividing families, but I think when he has character trying to hide the leather penis on their costume he's really just going for laughs around the theme of "wouldn't it be funny if women tried to be politically organised?"

Out of the three plays you mention, Antigone is the one I know least about. If you want to think of Antigone as a strong woman then that's not a terrible interpretation, but bear in mind that the result of her defying Creon is that she dies. Creon's life in the future isn't all roses (Athenian tragedy doesn't really allow anyone not to suffer) but he doesn't face divine punishment like characters who do wrong.

It seems that the general thrust of your question is something like why do Athenian plays have female characters at all, since women aren't supposed to be seen by men outside their family. I'd say three things in answer to that. 1: the tragedies aren't set in public spaces. They take place in private homes, and therefore where you'd expect to see women and where it is normal for women to talk to men. Although of course remember that the reason the people in these plays are being punished by the gods is for their errant behaviour, and therefore we can expect gender boundaries to be violated as part of this delinquency. 2: The comedies are often set in public spaces but they depict a world turned upside down, i.e. where women form their own government or private citizens conduct personal diplomacy with foreign powers, so you'd expect to see unnatural behaviour. 3: All the actors are men so when, for example Medea laments her lot in your quote, it's a man, playing an evil woman, who's saying those words.

I don't think there's any contradiction between Athenian theatre and what we know about the lives of Athenian women.

I'll try to answer the first question. From my readings of the plays you mentioned, and of Classical Literature in general, one can find the emergence of strong, subversive female characters in literature from various spheres such as 1. the Greek literary discourse at the time, 2. the Greek mythological discourse at the time, and 3. the sociopolitical role of women in cosmopolitan Athens (those characters you mentioned were almost always either queens or princesses).

1. The literary discourse:

Sophocles famously claimed that he portrayed characters as people should be, whereas Euripides portrayed them as they really were. So when Medea lashes out at society and grows jealous for what is essentially considered the norm at the time, she's being flawed and vindictive and purposefully unlady-like. At the same time, Plato's Book V of The Republic explores the role of women in society, especially in regards to women's education. He insists (through Socrates' dialogues) that the difference consists only in women bearing and men begetting children, this does not amount to a proof that a woman differs from men in respect of the sort of education she should receive; and we shall therefore continue to maintain that our guardians [and] their wives ought to have the same pursuits.” Again, “…their original natures are the same.” But of course, Plato also affirmed that this is possible in his Ideal state, a place where biological differences were not important and that on the realms of philosophy, women were STILL inferior to men, but had the potential to be MORE than what they really were in Athens at the time. It's likely that literary portrayals would have taken this into consideration when composing their work (and therefore be critical of social standards that would oppose it).

In Women Poets in Ancient Greece and Rome (2005), Ellen Greene points out that despite the marginal status of female poets, Sappho's reputation was unparalleled among critics even in classical periods, despite being considered only good for themes of the subjective and private spheres. While this is true, Greene points out that her poems did touch upon a very public sphere pertaining to the matters of the State. All of that shows just how strong the otherwise 'suppressed' female voice was in the literary discourse back then.

You also have to consider that when the Tragedians wrote Oedipus Rex or Medea, they were pretty big on philosophical dialectics, and so they were continually trying to show the plight of The Trojan Women or reinterpret and reimagine Homeric and mythical heroes in more contemporary contexts that furthered the narrative. Jason and the Argonauts has Jason be the hero, but Euripides purposefully portrays him in a different light. Agamemnon was, for all concerns, still considered 'heroic' but his masculinity is subverted by the time we see him in Orestes or Electra. There was a prevailing desire to continue the narrative from what was already there: We see Oedipus during his fall, rather than during his height, and that automatically necessitates a subversion of the gender roles.

2. The mythological tradition:

Those characters do come from preexisting mythology. Stemming from folktales of empowered female characters, necessitated those portrayals. Helen may be passive but she was still a very strong and overpowering symbol, almost a goddess in her narrative presence. But when you write a play about Medea you have to show her as the audience knows her to be from the existing myths. As a result, you have a Medea who is angry, jealous, and frighteningly subversive.

3. The socio-political role of women:

In Athens, this was was complex and wasn't simply about all women being grouped into one silent category. Edward Cohen (2015) points out in Athenian Prostitute: The Business of Sex, that there is a great divide between actual extant statistical data as to the role of women in Athens vs. the generalized conclusions made about them today. It's true that women were minority citizens, they did lack a substantial amount of civic rights that men enjoyed, however the literary sources about them in comic, tragic, other forms are the only abundant supply of information that we have. He writes:

In contrast to scholars’ long acceptance of material from forensic speeches as valuable for an understanding of Attic society, comedy has only recently been gaining recognition as a useful source of information on the actualities of Athenian life. Although the fourth-century plays of Menander and his contemporaries constitute a genre centered (unlike earlier comic works) on the private lives of individuals, nineteenth-century scholars made almost no historical use of this so-called New Comedy, whose value as source material they deprecated. In part this disregard reflected the relative paucity of surviving material (which increased exponentially during the twentieth century as a result of fresh papyrological publications); in part it reflected the traditional academic fascination with Athens as a paragon of high culture (inhibiting interest in surviving literature that was perceived as low-brow popular pap).

Moreover, these comic sources point out:

"...valuable information on contemporary life contained in this material. Concurrently, a shift in academic interests has generated renewed attention to the social dimensions—romantic attachments, class conflict, gender issues—that form the subject matter of Attic New Comedy. Despite the distortions inherent in the authors’ pursuit of love and of laughs, the assumptions—of contexts and relationships—underlying fourth-century comedy provide insight concerning Athenian social practices. In particular, scholars have recurrently demonstrated how Menander’s comedies (in which prostitutes often appear) provide considerable information about Athenian life, offering even highly specific details about the laws of property and succession. For example, the marriage alliances in the Dyskolos—although fashioned to meet the exigencies of humorous scheme and artifice—replicate contemporary marital and inheritance practices. The structure (and even the amounts) of dowries in Menander’s work are consistent with arrangements epigraphically and historically attested.

He concludes:

Although Menandrian plots may be unrepresentative of the
actual daily lives of the overwhelming majority of the population of Attika (who presumably did not spend a considerable portion of their time at dinner parties celebrating the happy conclusion of social and familial strife), “what Menander offers us through his comic lens is an image of the life of the society as a whole and its central human relationships

All of this is to show that playwrights, even in classical times, were not blind to the social inequalities that women faced and for purposes of entertainment, portrayal, audience, and even social dialogue, would address those issues directly.

Of course, for the tragic figures, one has to keep in mind that they are ultimately punished for what opposing society.

Did/do other societies where women's rights are strongly curtailed and their voices kept out of the public sphere have similar expressions in art and literature?

I believe that's a question for another day, but since poets and writers are often concerned with voices that are both public and private, strong and empowering female characters have always emerged if for no other reason than realism. In French literature you have the works of Christine de Pizan collecting these public-private voices in her essays. But even if you consider the oral tradition or mythology before the literature, there are strong female characters. I think a lot of it has to do with the fact that folktales would have had female authors who went unnamed.

I hope that answers some of your questions, or at least gives you a way of answering some of them! Those books are quite helpful even beyond just the portrayal of women since they also deal with women poets, and women in Athens in general.

Can I ask a follow up question specifically about Lysistrata? The play takes place during the Peloponnesian War in essentially a city under siege. Is there any way of knowing whether the war itself affected the freedom or rights of women in Athens? Either through the number of men being killed in war or just because of the pressures of the war itself?