Where It All Goes Down
Okay, let's see: we've got a librarian, a guy eating poems, and some burning dogs climbing up the stairs. Suffice it to say that we can't exactly pin down any sort of conventional setting in "Eating Poetry." Are we in a badly-run library, or a really nice animal shelter? The presence of the librarian and the poems suggests that we're in a library, where there's lots of poetry to be found (or eaten).
Strand is known for having these kinds of dreamlike settings that are difficult to categorize. And since he writes a lot about individuals struggling in their own metaphorical darkness, it makes sense that he wouldn't have any cookie cutter settings. So instead we see settings like libraries suddenly take on a more surreal look with burning dogs coming up from the basement and a weeping librarian stamping her feet.
So yes, we're more than likely in a library, but don't expect the goings-on here to look anything like your local neighborhood reading spot. Instead, it's better to think of this library as resembling our speaker's mind. As the setting shifts between joy and surrealistic darkness, we're asked to think of our speaker's changing mood. In the end, the dark setting is something that the speaker can embrace and romp around it. Poetry's transformed him, just as it's transformed the library he's now playing fetch in.