One good way to look at this is to think about the main conflicts that occur in the story. There is the conflict of Emily not giving up her father's body, the conflict of the alluded to fact that Homer was "not the marrying kind," and so probably was going to leave Emily, and the conflict with the aldermen about the taxes and the smell. So, if you look at each one of these conflicts you can tie them to a character's personality traits that led that conflict.
Emily's reliance upon her father's care and love, and her father's over-sheltering of her, led to her refusing to give up her father's body. Emily was naive, sheltered, and overly-reliant on her father's presence. This trait led to that conflict. Her father being a bit of a southern snob, and sheltering Emily too much tied into it also.
Homer Barron probably not sticking around to be Emily's beau can be tied to his lack of desire to marry, and to the fact that it was hinted that "he liked men." His not wanting to be with her probably led to the conflict of her old abandonment issues flaring up. Because Emily had the traits of abandonment issues in the first place, and possibly the family genetics of some crazy genes, Homer died.
The clashing between her and the alderment over the taxes and the smell can be linked to her trait of having southern pride, haughtiness, and ignorance.
If you look at the conflicts in the story closely, each one can be tied to the traits of Miss Emily, and other key players in the storyline. I hope that those thoughts help a bit; good luck!