My explanation for the film

Stories that inspired the idea for the film:
The Little Mermaid (The H.C.Anderson version, not Disney)- note the mermaid moments, the two timing with a brunette and betrayal, the knife, stupid suicide.
The Odyssey by Homer- see Sirens (explained further down), lone traveller, the paintings, greek/roman mythology references
The Rober Bridegroom (Brothers Grimm)- male lead character is a thief, hidden and mysterious rooms with dark secrets, scary older men, women pretending and playing roles

My take on the meaning of the film and character motivations:

A) I think they were a bit supernatural, but their mortal halves messed them up. Their beautiful, mysterious, disappearing mother. The father who believed and wrote about (and tortured into the mind of his daughters) metaphysical powers and states of mind. The consistent ever present image of THE SIREN. Basically, these two girls are of Siren heritage, or have grown up in an isolated environment with only Siren motifs surrounding them, and the memories of their past haunting their every waking moment. They are capable of super-human powers (or just telepathy), are literally haunted by trauma and poltergeists (negative energy taking form), or playing with mild schizophrenia. I think they are related to the sirens for all intents of this film, but have to live in a human world, the modern one, where Greek heroes are long since gone, and society has no real place for mythological beings to survive.

In the film, every time Violet or Grace seduce, you hear sea animal sounds (sounds like orca whales). Their desire is to be similar to the (Greek myth) Amazons in their use for men- seduce, gain a child, toss away the man.

Violet is the more timid of the two, forever in a childhood state because of her trauma. It is mentioned that Violet dreams of being normal, and desires a Little Mermaid type story (more Hans Christian Anderson tragic than a Disney film), in order to grow legs and leave the island of solitude that is their home. Violet knows she is not normal, and although both parents died too young and left her.

Grace was adored and needed to continue to be adored, but she was also the more powerful one, and tiptoed the line between genius and insanity. Grace is a firestarter, and closer to her mother's possible mermaid type of heritage. Grace is only financially set, she has little desire to explore the outside world and needs to control everything and everyone.

They are either related to, ancestrally, the sirens themselves, born to a mermaid mother who abandoned them, or have just developed into sort of witches/enchantresses with poor mental and emotional stability.

Look carefully:
"In Greek mythology, the Sirens were dangerous and beautiful creatures, portrayed as femme fatales who lured nearby sailors with their enchanting music and voices to shipwreck on the rocky coast of their island.Their number is variously reported as between two and five. In the Odyssey, Homer says nothing of their origin or names, but gives the number of the Sirens as two.The Sirens might be called the Muses of the lower world. Walter Copland Perry observed: "Their song, though irresistibly sweet, was no less sad than sweet, and lapped both body and soul in a fatal lethargy, the forerunner of death and corruption." Sirens combine women and birds in various ways. Later Sirens were sometimes depicted as beautiful women, whose bodies, not only their voices, are seductive"- wiki

Notice that the father hurts the younger Violet by crushing a bird, because she can't play her flute/music with real feeling. Tone death is not a siren trait as far as he is concerned.
They love water tales and baths. They create an island (a deadly one to lull and wither away on) for homeless, sexy travelers. They are surrounded by memories almost as physically present as the rotting corpses on the island of the sirens (rotting because the sirens did not cannibalize in the myths, simply doomed a man to die from his own stupidity...like in the film...I mean who puts himself on fire???)
The paintings in the forbidden room- beautiful women+birds+mermaids+the sea. The stories- they talk about the Roman god of the sea (Pluto aka Poseidon aka grandpa of mermaids). The hints are endless. Finally- the phrases that they quote randomly and wisely; many of them are small parts nabbed from the Odyssey when the sirens sing.

They should have named this film "Siren Song"..the double meaning of that phrase would have been more suitable.

Imagination, in all one does, is key