In the Greek myth of Oedipus the King, are the children he has with his mother?

Actually they are his children and half-siblings.

Step-sibs are relatives by marriage only and do not share any blood/genetics and the relationship ends when the marriage does, half-sibs share a parent and are still sibs if the marriage ends.

So Oedipus, son of Jocasta, marries his birth mother and has children with her--Antigone, Ismene, Polynices and Eteocles. Since Oedipus and his children all have the same mother but different fathers, they are half-sibs and since he's also their father, they are his children---who needs soap operas, the classics have 'em beat!

Oedipus......and he's a fictional character in a pair of performs by way of Sophocles: Oedipus the King (or Oedipus Rex) and Oedipus at Colonus. this is a enormously unwell tale. Sigmund Freud even coined a term the place a guy is warm for his mom....the Oedipus complicated.

Both. If a pair of twins marry each other, they're children are brothers and sisters, regardless of which couple they come from. They would have the same genetic makeup.

Well they would be his sons and daughters, and I guess his step brothers and sisters, they had the same mother but different fathers.

Both his children and his step-siblings.