The concept of Hell is a Christian one and Oedipus Rex was first performed ca. 429 BC, over 400 years before the birth of Christ; therefore it does not mention Hell.
The notion of an afterlife was rather indistinct in the classical period. Some mythological accounts distinguish between the Elysian Fields, which are a reward for heroes after death, the normal underworld, and Tartarus, which is a place of punishment, but these carry none of the importance that the afterlife does in Christianity. One cannot imagine an ancient Greek mother telling a child to be good or be sent to Tartarus. Instead, appropriate burial rituals are mainly aimed at preventing the dead from wandering the world as unhappy ghosts and letting their souls travel to the underworld.
Oedipus is concerned with issues of dishonor and ritual pollution. People who offended the Greek gods, especially by crimes involving killing members of their families, were pursued relentlessly by the Furies while still alive. Also, Oedipus is concerned with his actions bringing dishonor to himself and his family, something very important in the shame culture of ancient Greece. At the end of the play, Oedipus is not concerned about his own death, but more about the effects of his actions on his children.
The main point about death in the play is that we cannot know what sorts of reversals of fortune our lives will bring until our lives end. Thus the chorus concludes the play with the statement:
So while we wait to see that final day,
we cannot call a mortal being happy
before he’s passed beyond life free from pain.