The only "Siren" that exists in this game is an item that, when used, immediately forces you into a battle with that location's rarest monster formation. Aside from occasional bestiary hunting, the main reason people collect these is to use them in a certain room in the final dungeon, where it summons 5 Flan Princesses, which have a ridiculously low chance of dropping a Pink Tail that can be turned in for an Adamantite Armor (in TAY, it's turned in for a Pink Armor).
With regards the mythological reference, the Sirens themselves were originally a hideous and frightening combination of bird and woman; which portion of their form was female, and which parts were bird, varied depending on who was telling their description. It was their voice that lulled men too close to their island - an irresistible melody that was by turns sweet and sad. This makes sense, as in real life the singing of birds is generally considered to be pleasing (unless you're trying to sleep).
It was this sound that would seduce and hypnotize sailors, who would inevitably crash their ships against the rocks while searching for the source of it; if any men managed to survive the shipwreck, the Sirens would abduct them, carry them to the heart of their meadow-island, and kill them.
Over the years, as more cultures began to adapt portions of Greek Mythology into their own mythos, the Sirens changed form; to the Spaniards, they were a form of mermaid, and later on in Europe they became fully human females, who lured men with their sexual form as well as their voice. Sometimes they carried instruments, most notably a harp, although this was most likely the result of their confusion with a different woman-bird being called the Harpy; unlike its Siren counterpart however, Harpies mainly only steal food and small valuables.
Regardless of their form however, the intent of a Siren is to override good judgment and bring men to their own demise - so if they were to be depicted as a "sexy female" it'd almost make more sense if they WERE censored, in order to make the "tease" that much more alluring.