Satan is an embodiment of antagonism that originates from the Abrahamic religions. Since then, those religions have used Satan to refer to the Devil.
In "A Picture's Worth a Thousand Bucks", Satan appears in a scene when Peter Griffin said he would sell his soul to be famous. Satan was about to make his claim, when his secretary told him that Peter had already sold his soul for Bee Gees tickets, and again for half of a Mallomar. Satan asks for a lawyer, and everyone in Hell raises their hand.
He is mentioned in "And the Wiener is..." when Peter and Chris are attacked by a bear and Peter aims his gun at the bear and tells him to say hello to Satan.
In "Peter's Daughter", Stewie and Brian were not able to renovate the wrecked house, so Stewie decided to blow it up. They got out the house in time, but forgot that the electrician they hired was still inside. Stewie says to Brian he will be going to doggy hell. Satan is then seen scaring dogs in Hell with a vacuum cleaner.
Satan takes exception to Stewie's Nick from The Great Gatsby taking credit for the deviled eggs in "High School English".