"I will search and clear this darkness." What is the significance of this quote for "Oedipus Rex"?
Darkness in "Oedipus Rex" is - like most of the themes in this fascinatingly complex play - completely paradoxical. As a symbol, it's associated with two opposite things.
Shortly before Oedipus says this (to the Chorus, early on the play) the Chorus mention the "dark-songed Sphinx". Darkness is associated with mystery - Oedipus solved the riddle of the Sphinx, its "dark song" and ended its reign of terror over Thebes. Oedipus now promises to clear the darkness of the plague - by finding the murderer the oracle claims is responsible for it. Darkness, then, is negative - and light is positive.
Except that, when Oedipus discovers the identity of the murderer, it is him, and in shame he blinds himself. Everyone throughout the play tells Oedipus to stop his search and give in, and to be happy with what he has - to enjoy, if you like, the darkness of ignorance. Enlightenment leads to blindness, and so the "light" is - literally and metaphorically - dark.