In the Wikipedia page that you link, they all seem to be related to the gods or the supernatural.
As I understood the myth, the Siren is a symbol for the lure of the sea; men feel attracted to the sea despite the danger it poses. The mermaid is similarly used to symbolize the attraction of the sea. There is a difference, the temptation posed by a mermaid is the beauty of her body, the temptation of a Siren is in her voice. Depicting the lure of the sea as a desirable woman works as a great narrative device.
So the Sirens have a supernatural origin, and their power is supernatural. Their seductive magic is in their voice, so they don't have to be beautiful - or Odysseus would have required his men to not only stuff their ears, but also wear blindfolds.
When depicting Sirens, it makes sense to depict them as beautiful women to make it more immediately clear to the audience that they are temptresses. But this was not in the Odyssey.