Songs With Two Sides
You'll notice that Atwood has a lot of poems with "Song" in the title. That's not to say that they sound singsong in any way, but rather they sound like songs because they're lyrical explorations of what it means to be two things at once. What does that mean? Simply put, you'll see that Atwood likes to explore themes of being on both sides of the same coin: male-female, nature-man, self-other. You'll see a lot of duality (opposing ideas) that tend to isolate her speakers from the world around them, not unlike those Sirens trapped on that "picturesque" island.
Feminist ideas also echo in much of Atwood's work, but you'll also notice that her protagonists (usually female voices) are never pushovers or passive victims. They may suffer, but they do so in order to better understand the world around them. To top it off, Atwood often has a wonderful sense of humor and wit in her poetry that doesn't wallow too much in self-pity. She'll throw in a few ironic twists (like we see in "Siren Song") that tend to make light of the whole thing, no matter how severe the circumstances may be.
For a better idea of her style, check out these gems: "Bull Song," "Carrying Food Home in Winter," "Song of the Worms."