We're a long way from the eighth century BC, so it's fitting that Atwood would choose to bring "Siren Song" up to speed with free verse, rather than the normal dactylic hexameter that we usually see in epic poetry. After all, her speaker isn't speaking to Odysseus anymore. She's speaking to folks like us, who have shorter attention spans (and less skill with a spear) and need to hear the point sooner than later.
So, we have nine stanzas with three lines each (which fits with the traditional number of three Sirens) and lots of enjambment (lines flowing into one another without punctuation). The lines themselves are short, sweet, and to the point, like what we see in line 7: "the song nobody knows." Nice and simple, right? The enjambment between lines and stanzas also helps to maintain the speaker's casual and informal voice. She's not lingering over her words too much or getting super-dramatic at any given time with lots of "Ah's!" or "Oh's!" Instead, she's keeping us in suspense by carrying our reading eyes over from the abrupt end of one line into the start of the one right after. Check out lines 21-22 again to see how she breaks up "this song" ("This song what?" we demand to know) with "is a cry for help" ("Whew! We finally found out"). The use of enjambment here builds suspense and draws us deeper, and more unwittingly, into the Siren's song.
But that's not all. She's also telling us her little story by using anaphora. By repeating clauses like "the song" and "only you," we get that poetic vibe without being hit over the head with perfect meters and rhymes. So, we feel a bit freer with this "Siren Song," which makes us we feel as if this Siren-speaker is speaking plainly to us. She could even be someone we know (excluding the whole luring sailors to death bit). Of course, that's all part of the deadly allure, as we find out at the end of the poem.