What is the major conflict of the play Oedipus the King (or Oedipus Rex), and the moral connected to the conflict?

In Oedipus Rex (or Oedipus the
King), the major conflict exists based upon what Oedipus has unknowingly done in his
life to wreak the havoc (in the form of plagues) that now visits
Thebes.

Before Oedipus was born, his fate was already decreed: he
would kill his father and marry his mother. The gods are responsible for defining his actions
before Oedipus takes his first breath.

To avoid the fate the gods
have ordained for the King of Thebes (believing they can do so: the major theme in the story),
Laius and Jocasta agree that the child she has delivered be killed. Oedipus is taken with
instructions that he be disposed of, but the soldier has not the heart to do so. He abandons the
baby, believing the infant will die. Oedipus is found and taken in by a shepherd, and ultimately
finds his way into the palace of the King of Corinth, who adopts the baby and raises Oedipus as
his own son. Oedipus has no knowledge of any of this.

When Oedipus
crosses the path of Laius and his slave, they insult and attack Oedipus, without knowing who he
truly is. Oedipus defends himself and kills Laius, thus (unknowingly) fulfilling the first part
of the prophecy.

Oedipus later solves the riddle of the Sphinx who
has terrorized the people of Thebes (and all travelers in the area) for a very long time; in
doing so, Oedipus is hailed as a hero, and it is suggested that he marry Jocasta, Laius' widow.
Oedipus agrees, once again unknowingly fulfilling the second part of the
prophecy.

He and Jocasta have two children, Ismene and
Antigone.

Years have passed, and plagues have befallen Thebes. The
oracle ("fortune teller") explains that the cause of these calamities is the murder of Laius that
has never been solved. Oedipus, a good and just king, orders that the culprit must be found and
punished.

Herein, I believe, lies the main conflict of the story:
the plagues must be stopped and the murderer found. However, the murderer is, unbeknownst to all
of them, Oedipus. And Oedipus will have to own up to what he has done, if he is truly a just and
noble man and king, although at first he does not believe what he
hears.

Based upon Sophocles (the author) and his culture's system of
beliefs (predestination), the moral of the story is that you cannot evade or escape your fate: it
will catch up with you, and there is nothing you can do to stop it.