How were women characters portrayed in 20th century literature (novel and plays)?
Women characters are portrayed in all sorts of ways in 20th-century literature. Of course, there are trends that can be identified and discussed.
The nineteenth-century (Victorian) ideal of "the angel in the house" is not dead, but it's much more commonly the case to see in 20th-century literature women who have minds and lives of their own. The 20th century did not invent the idea that women should have equal rights, of course, nor the idea that injustices against women should be the topic of literature. (For example, some ancient Greek plays can seem amazingly modern on these topics.) What 20th-century literature does often offer is more direct and open and frequent presentation of these ideas. Women are not as frequently presented as the "shrew," are more frequently presented as fully human (e.g. with fantasies and sexual desires of their own), and so on.
These changes are due in part, I'm sure, to voting rights being extended to women in the early 20th century in many countries, to women's more general access to education, and to the continued growth in the number of women writers.
This is a fairly broad question. I am not certain any one particular answer can suffice. There might be other answers that help to give some light, but in the final analysis, I think additional research and detail will be of critical importance to your answer. One way in which women characters have been depicted has shown the balance between what society has told and what their own individual hears might desire. The idea that women are "forced" to fill a role as opposed to what can be done or what actually wants to be done has been a theme of women's depictions throughout 20th century literature. This has also developed a greater sense of empowerment within women characters and a greater sense of autonomy and control over both senses of self and their places in the world.