How important do you see the messenger and the shepherd were to the storyline?

The Messenger from Corinth arrives to tell Oedipus that his father, Polybus, is dead, and that the people of Corinth wish Oedipus to be their new king. He also reveals to Oedipus, however, that Polybus and Meropé are not his real parents. He says that long ago a stranger from Thebes gave him a baby as a gift to the king and queen of Corinth. This baby was, of course, Oedipus who would grow up to be king himself. The Messenger, then, provides the audience with the first real clue of dramatic irony that suggests that Teiresias' words (and those of the Oracle) are true - long before Oedipus discovers their veracity.

The Herdsman gives Laius' and Jocasta's baby to the messenger upon their orders - and is also the same man who witnessed Laius's death. When he returns to Thebes and sees that the man who killed Laius is the new king, he asks leave to flee from the city. Oedipus sends for him when the messenger alludes to his intimate knowledge of the crime, in the hopes of discovering the identity of his true parents. He then reveals that the baby he gave to the messenger was Laius and Jocasta's son, adding one of the last pieces to the puzzle that will implicate Oedipus as the source of the kingdom's plague.