As immortals, they would not need jobs and would be superior to people; who do. They would not have jobs, but the Greeks would have loved stories about them moving among people pretending to have mortal jobs to play tricks upon humans and to obtain what they wanted out of us.
my favorite characters from greek mythologies would be Aphrodite: model, actress, singer, talk show host, anchorwoman, any kind of celebrity that depends somewhat on her physical appearance/appeal.