Most of the elements are indeed taken from Greek Mythology however they've been put together in a different manner. I'll try to outline a few changes:
Perseus did indeed kill Medusa and save Andromeda, however in the myth it was a sea monster sent by Poseidon not Hades, it was indeed based around the city of Argos.
Medusa was actually one of three Gorgon ...
The movies are loosely based on Greek Mythology. There are a lot of faux pas in the movies which makes them fun to watch, but not accurate to the mythology. Here are a couple of sites which explains some of the issues:
Mythtakes About the Movies
When Hollywood Gets in the Way of a Perfectly Good Myth
Even Hollywood movies based on true events are just "...