The overall sound of "maggie and milly and molly and may" is similar to a nursery rhyme, with those dactyls and anapests in lines 1 and 11, that we're tempted to call it one. We get perfectly end rhymedcouplets like lines 11 and 12 ("me" and "sea"). Then we have alliteration going on, with "sang/ so sweetly" (3-4), "stranded star" (5), and a crab "blowing bubbles" (8). All of this lends a singsong sound to the poem. It's like we can't help but hear our elementary school teacher's voice throughout.
As well, we have a ton of enjambment between the lines, which keeps things moving forward in the free and imaginative way a kid would tell a story. Adding to that speedy sound is the repetition of "and" glued to the punctuation marks at the end of lines 4 and 8. This leaves no room for pausing, so the poem sounds just like any small child repeating a story: "and then Chucky threw the football and then it went through Mr. Grump's window and then we all ran and hid under the porch and then we got mud on our pants and then..."
The net effect of these sonic choices is a tone of innocence and sincerity. That kind of sincerity makes the speaker's simple sophistication all the more poignant, since we're not set up to expect any big ideas about life, and yet—whammo—we get just that in the final couplet.