OK, first things first. What makes the writing style of Libation Bearers poetic? On Shmoop, we use the translation by Christopher Collard in the Oxford World Classics series. We like this translation a lot, but it actually covers some things up from the poetic standpoint. As you'll see if you use this translation, the dialogue between the different characters is in prose, whereas the songs sung by the Chorus (plus some of the set-piece songs involving, say, the Chorus, Electra, and Orestes) are in verse, which he makes into a kind of free verse. This is half-way right, except that in the original, absolutely everything is in verse, including the dialogue between characters. Collard can get away with putting the ordinary dialogue into prose, though, because the poetic meter during the dialogue is a pretty basic one, so called "iambic trimeter," which Aristotle called the one closest to ordinary speech.
What about the songs by the Chorus? There's no question that these are the play's poetic showstoppers. You can also see this in the fact that they use much more high-octane metaphorical language than the rest of the play. Sometimes, these images can be really weird, like at lines 392-394, when the Chorus says that "my heart's anger / is blowing fiercely from the prow, / in rancorous loathing." Here, they seem to be comparing their heart (or perhaps the "front of [their] mind" from a line earlier?) to a ship sailing through an ocean of anger that is frothing at the bow. Images like these are very cool, but hard to put together, and require a lot of imagination.
This brings us to our final adjective: subtle. The subtlety of the play comes throughout, not just in the Chorus's songs. Often times, you have to pay as much attention to what is not being said as to what is. (This sounds tricky, but don't we do the same thing in conversation all the time?) An example of this is Orestes's final dialogue with Clytemnestra, which basically centers on Clytemnestra's sex life, though of course neither character would put it in such blunt terms.