Below are elements that characterize the different genres. Each or several can be analyzed to provide insight into a work within the particular genre. Some definitions are available at the links.

Fiction
Plot
structure
setting
character
point of view
language (diction, sentence pattern)]
style (metaphor, simile)
theme
irony
symbol

Poetry
Voice: Speaker, tone
Diction: denotation, connotation
Imagery
Figures of speech
symbolism
irony
syntax
Sound: rhyme, alliteration, assonance
rhythm/meter
Structure: closed and open form
theme

Essay
voice
style
thesis
structure

DRAMA
characters
dialogue
setting
plot