If the only available minyan to hear Megillat Esther is a mixed minyan with no mechitza, can one attend the minyan or is it better to not hear megilla at all? Would it matter if the baal megilla was a male or female? Or if the person hearing the megilla is male or female?
It appears from the discussion in some Ashkenazic Achronim that a woman's mitzva is to hear a megillah reading, whereas a man's mitzva is to read a megillah (which can be fulfilled by listening to someone else fulfill their obligation). As men have a higher level of obligation, it can only be fulfilled by listening to someone with a greater than or equal level of obligation -- thus a man should really hear a man's reading.
If a man is stuck someplace and his only option is to hear a woman reading megillah, well if he can take a megillah and more or less read the words himeself (cantillation notes aren't critical), better to do that. If the female reading is truly his only option, then I strongly presume he should go ahead and listen to that, as many Achronim will say he's still fulfilling his obligation.
As for the mixed reading: In the second half of the twentieth century many great American rabbis felt the need to strongly demarcate between the Orthodox and Conservative movements, to the point of saying that an Orthodox fellow should not attend a non-mechitza Rosh HaShanah service, even if that means missing shofar blowing altogether.
With regards to megillah reading -- often the reading is freestanding and not part of a prayer service; and a minority opinion would even count women for a "minyan" vis-a-vis the extra blessing at the end of the reading; hence I'd suspect there would be strong room to say better to hear in a mixed crowd than not to hear at all. If the reading was part of a non-mechitza prayer service in a heterodox synagogue it would be a lot more of a problem. (Better yet, if the reading is held in someone's home and not open to the public, or a rare event, then the mechitza is a preference but not a requirement -- see here for more.) If one has the option of reading their own megillah, you'd have to weigh the value of a non-mixed reading against the value of having a big crowd for the mitzvah.
I'm somewhat confused by the premise of the question. I've been to megilla readings in school auditoriums, in people's living rooms, and other places outside the shul. There is no inherent connection between hearing the megilla reading and a shul setting, and as such I don't see why there should be a requirement for a mechitza during reading.
If you have sources that state otherwise, please let me know! It would raise the question of how the readings in other locations should be conducted.
Rav Shlomo Zalman Auerbach is qouted in Valehu Lo Yibul 1:430 as holding that a mixed reading it is prefable to have the men and women sit separately. This was a case of a mixed reading in the army. It is noted that it seemed that Rav Shlomo Zalman held that if they say together it wouldn't be m'akev.