Mythology

Although the overall story is not taken from any mythology; a lot of the characters are based on Greek stories.

Dionysus/Bacchus
The Greek and Roman God of Wine, Ecstasy & Party. In the film the film the character Denis (owner of the Cool Club) says a speech about wine. The speech is a modernised a version of:
Athenaeus, Deipnosophistae 2. 63a-b
...Euboulos makes Dionysos say: ‘Three bowls only do I mix for the temperate – one toe health, which they empty first, the second to love and pleasure, the third to sleep. When this is drunk up wise guests go home. The fourth bowl is our no longer, but belongs to violence the fifth to uproar, the sixth to drunken revel, the seventh to black eyes. The eight is the policeman's, the ninth belongs to biliousness, and the tenth to madness and hurling the furniture. Too much wine, poured into one little vessel, easily knocks the legs from under the drinkers.’"
Pandora
Pandora was the first women on earth and is the first women to appear in the film.

When Prometheus stole fire from heaven, Zeus took vengeance by presenting Pandora to Epimetheus, Prometheus' brother. With her,Pandora had a jar which she was not to open under any circumstance. Impelled by her natural curiosity, Pandora opened the jar, and all evil contained escaped and spread over the earth. She hastened to close the lid, but the whole contents of the jar had escaped, except for one thing which lay at the bottom, and that was Hope.

John William Waterhouse: Pandora - 1896

In the film Pandora opens her box to give Dylan a card for The Cool Club. 

Echo and Narcissus
Just before Dylan finds The Cool Club he encounters these two odd characters, Neville and Echo. Before Dylan enters the scene, Neville asks Echo if she wants to go to the gym, she echoes "the gym" with annoyance. Neville starts to leave when Echo see's an old photo of them happy together. She puts down her fast food and goes to cuddle Neville. He shouts, "Get those greasy hands off me! I would die before I let those hands touch me". 
Echo replies "let those hands touch me" staring with love at Neville's hands. 

The two characters and their dialogue is based on the following:


METMORHOSES BOOK 3, TRANS. BY BROOKES MORE:
CADMUS AND THE DRAGON, THE HOUSE OF CADMUS
[370]One day, when she observed Narcissus wandering in the pathless woods, she loved him and she followed him, with soft and stealthy tread.—The more she followed him the hotter did she burn, as when the flame flares upward from the sulphur on the torch. Oh, how she longed to make her passion known! To plead in soft entreaty! to implore his love! But now, till others have begun, a mute of Nature she must be. She cannot choose but wait the moment when his voice may give to her an answer. Presently the youth, by chance divided from his trusted friends, cries loudly, “Who is here?” and Echo, “Here!” Replies. Amazed, he casts his eyes around, and calls with louder voice, “Come here!” “Come here!” She calls the youth who calls.—He turns to see who calls him and, beholding naught exclaims, “Avoid me not!” “Avoid me not!” returns. He tries again, again, and is deceived by this alternate voice, and calls aloud; “Oh let us come together!” Echo cries, “Oh let us come together!” Never sound seemed sweeter to the Nymph, and from the woods she hastens in accordance with her words, and strives to wind her arms around his neck. He flies from her and as he leaves her says, “Take off your hands! you shall not fold your arms around me. Better death than such a one should ever caress me!” Naught she answers save, “Caress me!” Thus rejected she lies hid in the deep woods, hiding her blushing face with the green leaves; and ever after lives concealed in lonely caverns in the hills. But her great love increases with neglect; her miserable body wastes away, wakeful with sorrows; leanness shrivels up her skin, and all her lovely features melt, as if dissolved upon the wafting winds—nothing remains except her bones and voice—her voice continues, in the wilderness; her bones have turned to stone. She lies concealed in the wild woods, nor is she ever seen on lonely mountain range; for, though we hear her calling in the hills, 'tis but a voice, a voice that lives, that lives among the hills.