There are quite a few oxymora present in Sophocles' Oedipus Rex. We can especially see many in the opening speeches in the play.
One is present in Oedipus's opening line, "My children, new sprung race of old Cadmus" (1). Cadmus is recognized as the founder of Thebes, four generations prior to Oedipus's reign (eNotes, see note). King Laius is Cadmus's great-grandson. The oxymoron in Oedipus's line is that he refers to the Thebans as the "new sprung race of old Cadmus." In other words, he refers to Cadmus as old, who is four generations older than Oedipus, but still refers to the Thebans as the "new race," creating irony and an oxymoron.
A second oxymoron can also be found in Oedipus's opening speech when he refers to his citizens as filling the city with the "sound of hymns and groans" (5). This is contradictory because hymns are musical and used in worship. They can be both sad and happy. While groans are low moans of intense pain. Since groans of pain stand in great contrast to music, we can easily see that the phrase "hymns and groans" is an oxymoron.
Another oxymoron can be seen in the Priest's long speech in reply to Oedipus's opening speech. As the Priest describes the plague, he especially describes the famine in the line, "There is death in the fruitful buds," meaning that the blossom buds that would bear fruit have all died (27). However, this phrase as it is spoken is an oxymoron because it combines death with the phrase "fruitful buds." Buds either bear fruit or they do not; therefore, pairing fruit with death is an oxymoron.