I think you could pick several themes out of this story... perhaps a typical "man versus society" theme would work... although in this case "eccentric, upper-class woman versus small town" would work...
The antagonist was Miss Emily's dad because he denied her male compionship so she became desperate for human love and desperate enough to commit murder and cover it.
There are many conflicts but the three biggest are Emily vs reality, Emily vs her father, and Emily vs herself. In vs reality, Emily doesn't seem to except that, among other things, people will leave...