In "Why I Live at the P.O." why is the character of the sister funny?
I assume that your question refers to the narrator of this excellent and amusing story, rather than Stella-Rondo, who is the sister of the narrator, and is referred to as "Sister." It is important to note the point of view adopted by the author in this story. Using the first-person point of view allows us to see things from Sister's point of view, but it also presents us with a limited narrative as we only see things from her point of view. Thus Welty reveals a character who is so dominated by competition and envy with her sister that the credibility of her narrative is often compromised. Part of the humour in the presentation of Sister lies in her own presentation of her woes and her self-pity, something that she is unaware of. Thus her presentation of her relationship with Stella-Rondo, whilst it may be true in terms of its depiction of her and her manipulation, also is humorous in the way that the narrator views her own situation:
So I hope to tell you I marched in and got that radio, and they could of all bit a nail in two, especially Stella-rondo, that it used to belong to, and she well knew she couldn't get it back, I'd sue for it like a shot. And I very politely took the sewing-machine motor I helped pay the most on to give Mama for Christmas back in 1929, and a good big calendar, with the first-aid remedies on it. The thermometer and the Hawaiian ukulele certainly were rightfully mine, and I stood on the step-ladder and got all my watermelon-rind preserves and every fruit and vegetable I'd put up, every jar. Then I began to pull the tacks out of the bluebird wall vases on the archway to the dining room.
Here we see Sister's joy and satisfaction at making a real statement by taking everything that belongs to her, even though she will clearly have little use for so many of the things she is taking. She is shown to be a rather childish, immature character, even though we can definitely see that she has been wronged by Stella-Rondo.