What is the style used in "Eating Poetry" by Mark Strand?

Regarding the style of "Eating Poetry," one could classify it according to the genre of poetry, the movement, or the mood and tone. All of these are ways of addressing the "style" of a given poem.
The genre of this poem is free verse. Free verse does not conform to any specifically defined number of lines or a rhythmic/metrical arrangement of words. A poet using free verse can use any combination of line length, stanzas, or rhythms that he or she desires. In this poem, the author writes in three-line stanzas. The lines don't follow a prescribed rhythm like iambic or dactylic but, rather, follow the rhythms of natural speech. There are a few rhymes in the poem, notably in the last two stanzas, but there is no rhyme scheme carried out in the poem.
The movement the poem most closely adheres to is Modernist. Modernist poems favor the rhythms of natural speech over set rhythmic patterns. They also favor erratic rhyming patterns or no rhyme at all. Modernism began in the first decades of the twentieth century and continued on. This poem, while somewhat bizarre, is relatively straightforward and unambiguous, so it is not best classified in the Post-Modernist style. A Post-Modernist approach would be highly subjective, leaving more doubt as to the poem's interpretation, and it would use less structure in its punctuation and syntax than this poem does.
Finally, this poem uses hyperbolic and facetious humor. Although the speaker is obviously passionate about poetry, he treats his subject more flippantly than seriously. He uses funny exaggerations about his mouth dripping with ink and himself turning into a dog-like thing after reading poetry. The portrayal of the librarian as irate, unhappy, obtuse, and fearful of the speaker's love for poetry is satirical. The librarian is a foil for the speaker. Her disapproval of the speaker's voracious appetite for poetry serves to emphasize his passion. The way the poet expresses his thoughts about consuming poetry is funny and flippant.
One could describe the style of this poem as humorous Modernist free verse.