Assonance has been explained very well up above, so I’m going to tackle allusion. An allusion is when one work makes a brief reference to another work without explaining it in depth.
Even if you’re not familiar with allusions, you’ll see them all the time in works of fiction. For example, one of the episode titles in “Lost” is “White Rabbit,” a reference to “Alice in Wonderland.” Two characters on the show, Locke and Rousseau, are named after Enlightenment philosophers.
Many, many works of fiction have allusions to the Bible or to mythology. For example, the short story The House of Asterion by George Luis Borges is an allusion (or a reference?) to the myth of the Minotaur. It starts with a narrator describing the house he lives in, which starts to sound more and more like a maze. At the end of the story you realize the narrator is the Minotaur. This is different from an allegory, where one thing is a symbol or a representation of another thing.
Here’s an example from pop culture: Lord of the Rings allusions in Led Zepplin lyrics. There’s the song “Misty Mountain Hop” and these lines from “Ramble on” :‘twas in the darkest depths of Mordor, I met a girl so fair/ but Gollum and the evil one crept up and slipped away with her.”
So if you can convince your teacher that lyrics= poetry, you’re gold. Otherwise, I just googled “allusions in poetry” and came up with a few pretty good results, but I’m not sharing.
Try to pick something you like, because I smell another assignment just around the corner. I bet you a million dollars your teacher is going to assign you to analyze all the allusions in your poems after you hand them in.
You probably think this assignment sucks, but writers do this to add richness and depth to their fictional worlds… it can really make a work more rewarding. At least when you figure one out, you’ll get a clever “A-ha!” moment.