What's odd about Medea is not that she commits atrocious crimes, but that she is allowed to do so over and over. In the case of other mythical figures, such as Tantalus or Pelops, punishment follows, and the guilt from the crime becomes a curse which succeeding generations must reenact. Medea escapes unpunished. Perhaps this has something to do with her status, which lies uncomfortably somewhere between the divine and the human.
Some scholars have suggested that Medea was a minor goddess assimilated into the Greek pantheon, or perhaps some kind of vengeful daemon associated with childbearing. But it doesn't really explain the diversity of myths about her, or why she is consistently associated with particularly gruesome deeds which transgress the most sacred norms of Greek society: the bonds of family and guest friendship, respect for the gods.
In some ways Medea is the opposite of the Erinyes – instead of the punisher of those who slay their kin, she is the enactor of these abominable deeds, all of which seem to be strangely unmotivated. Even in Euripides, where she is allowed to argue her case, the murder of her children ultimately seems out of proportion to the wrongs done to her: The essential arbitrariness of the destruction, the sense that it happens without any particular evil intention on her part (or is this simply a result of the lack of psychological development in myth, the way it simply states facts and does not inquire too deeply into their causes?).