Medusa is a woman who had snakes for hair that
petrified anyone who she looked at. Athena turned
her hair into snakes as punishment for a relationship
with Poseidon. When she was killed, Pegasus jumped
out from her neck. Definitely a weird birth, but not
one of the weirdest in Greek mythology (looking at
you, Dionysus, popping out of Zeus' thigh).
The sphinx had the upper body of a woman, the lower
body of a lion, and the wings of an eagle. She would kill
anyone who could not answer her riddle, so she killed a
lot of people. Her riddle was "what has four legs in the
morning, two in the afternoon, and three in the
evening?" The answer is man, and the sphinx killed
herself when Oedipus answered the riddle.
Sphinx
The sirens lured sailors to their deaths by singing so
beautifully that the sailors would jump into the ocean.
Sailors who wanted to avoid this fate would have to tie
themselves to the mast of the ship and try to block out
the songs.
Sirens
There are many more amazing monsters beyond this list, so I encourage you to do
some reading on classical monsters!