What a wonderful story this is.
Three characters that drive the plot of "Why I Live at the P.O." by Eudora Welty are Sister (the narrator), Stella-Rondo and Mama. This is not to say that the other characters are not important as well, but I believe the combination of these three allows the other characters to behave as they do, which in turn, drives the plot.
First of all, Sister seems to be the voice of reason in this crazy household. She is the only one that is mentioned who has a job, even though it is a very "humble" job. She is also the only one who seems to do any work in the house. She cooks dinner and later puts up preserves. And she has no problem in "telling it like is." She is not a drama queen, she will admit to the truth and does not lie, and she is intuitive enough to read between the lines of her sister's lies.
The conflicts center around Stella-Rondo and her unexpected return home with her "adopted" child, Shirley T. (which would seem to be an allusion to Shirley Temple, a famous child-star of the 1930s). Stella-Rondo is, according to the narrator, spoiled. This seems to be supported by her behavior and the related behaviors of others towards her in the household. Stella-Rondo is a liar and an instigator of trouble. No one questions the "tall tales" she tells, which generally are directed at Sister, and cause Sister no end of grief at the hands of the other family members.
The third character that drives the plot is Mama. Knowing her children as she does, and having lived with Sister after Stella-Rondo ran off with Mr. Whitaker to get married, one would think Mama would be able to objectively see each child, "warts and all," for exactly who she is. Sister's actions speak louder than words, as do Stella-Rondo's. Sister contributes to the running of the household; Stella-Rondo contributes nothing but trouble and discord within the household from the moment she returns. However, as is the case with some people, Mama cannot see the truth staring her in the face. She automatically takes Stella-Rondo's side of things, and believes her stories when they are so easily discernible as lies.
Papa-Daddy and Uncle Rondo are also important in that they also buy into Stella-Rondo's lies and cause Sister misery. However, the three women appear to galvanize the plot with their actions. It is, of course, because of Stella-Rondo's lies and the family's belief in them that Sister finally moves out—to go and live at the post office.