This is a difficult question to answer for several reasons. First, it is difficult to know when the Trojan war took place. So, there will be considerable debate here. Second, there was a period called the "dark ages" in Greek history where there was limited writing on Greek civilization. Third, the Greek world was broad. So, it is difficult to make broad statements. For these reasons, it will be difficult to know anything about the role of women for certain.
In light of these three points what we have are primarily the works of Homer and what we know of classical Greek culture. Based on this little information we have we can say that women did not have too many rights from a social point of view. They were expected to keep in home and be faithful to the household and family. Penelope, the wife of Odysseus, might be the image of a "perfect" Greek wife. She was working on the loom and stayed faithful to Odysseus, even though Odysseus was not faithful to her.
We see a very similar picture in Athens in the speeches of Lysias. His speeches are important, because there are many incidental details of social life. For example, in his speech on the murder of Eratosthenes, we can see the very domestic life of women. Some scholars even question whether women were allowed at the theater. In short, the life of women before, during, and after the Trojan was was very oppressive compared to modern day.
To be sure there are counter examples of strong women, but they were the exception.