Medusa wasn't always a snake-haired, ugly woman. She was one of the Gorgon sisters and daughter of Phorkys and Keto, the children of Gaea (Earth) and Oceanus (Ocean). Her sisters were Sthenno and Euryale, and were immortal, whereas Medusa was mortal.
Originally, she was a beautiful maiden, and one of the priestesses of Athena. Part of being a priestess was adopting a celibate lifestyle (no boyfriends for her). Medusa followed this for many years, until she met Poseidon, and seemingly forgot her vows. They quickly fell in love, and got married. Athena was not pleased with this turn of events (they had even married in one of her temples!), and put a curse upon the beautiful Medusa.
Her hair (which is what had attracted Poseidon's attention in the first place) was turned into dozens of venomous snakes. The beauty that had defined her was gone. Medusa was driven out of her home, and was shunned and dreaded by the rest of the world. In her despair, she became a wanderer, and changed into a character worthy of her outer appearance. For the rest of her life, anyone she looked directly at turned to stone. Some myths say she moved to Africa and tried to cut the snakes off, but they grew back almost instantly. This myth also works to explain why there are so many poisonous snakes in parts of Africa.
Perseus was a Greek hero sent on a quest to kill Medusa. He was armed with a scythe from Hermes, and a reflective shield from Athena. Perseus used the shield to safely cut off her head, without looking directly at her. Perseus gave her severed head to Athena, who then mounted it on her shield.
The blood from her head fell into the sea, and from it came Pegasus and Chrysaor. Pegasus was depicted as a white horse with large feathery wings who could fly. Chrysaor was often depicted as a young man, although he eventually went on, became a king, and had some kids with strange deformities (think three heads) because of his mother's blood.
With a clear understanding of the myth, the poem makes a lot more sense. From what I learned, the poem must have taken place sometime during Medusa's exile. During that time, the people weren't fond of having a snake-headed person running rampant through their town, and often went off in search of her.
The allusion is a bit trickier. Although the original Medusa in the comics was named that, there was nothing else in common and it didn't count as an allusion. The newer one, however, does. The character looks more similar, and shares personality traits (greed, longing) with the monster from Greek mythology.
Overall, the three texts feed off of each other. The context of the poem makes more sense, and the references to Medusa are clearer with more background knowledge on the myth itself. The comic character that alludes to the myth makes sense by itself, but with knowledge of the myth, it is easy to see their connection, through appearance and overall personality.
Although all three parts can stand alone, they can all be better understood by combining them.