"Lady Day" (Billie Holiday) was a jazz singer, and jazz thrives on improvisation. Fittingly, the speaker of "The Day Lady Died" sounds like he's just making things up as he goes along. The entire poem is a factual narration of the speaker's afternoon, with very little in the way of figurative language or fancy descriptions. (The word "muggy" in line 6 is the only descriptive adjective in the poem). You might call the third stanza "The Golden Griffin Bookstore Blues."
From the perspective of sound, the goal of the poem is to leave the reader breathless by the time "everyone and I" stop breathing in the final line (line 29). For example, in the second line O'Hara could have easily put a period after "Bastille day" to give the reader a small pause; instead he adds the word "yes," forcing the reader to push on into line 3 without a pause.
In the third and fourth stanzas, he trips us up with a bunch of strange or foreign-sounding names," like "Stillwagon," "Bonnard," "Verlaine," "Strega," and "Ziegfeld." Thus, when he notes in the fifth stanza, "I'm sweating a lot by now," we're like, "We're right there with ya!" The last line includes the deliberately confusing reference to "Mal Waldron and everyone and I. .." O'Hara could have written, "Mal Waldron, everyone, and I," but he adds an unnecessary "and" to emphasize the rapid-fire nature of the speaker's thoughts. It's a sprint to the finish, and the speaker sounds like he's jumping from name to name like Spider-Man jumps from building to building. He doesn't decide where to go next until the very last possible moment.
Finally, how do the capitalized names affect the way you read the poem? We think they add an extra accent to those words, giving an effect similar to making "quotation marks" with one's fingers while speaking.