In any great work of literature there are arguably an abundance of themes, and this classic play is certainly no exception. So, in answer to your question, I am going to focus on one theme that to me stands out as being essentially important to the action - the gradual journey of self-knowledge that Oedipus embarks on through the course of the play.
Oedipus is certainly sincere in wanting to find the killer of Laius and thereby rid Thebes of its punishment and the plague that is killing its citizens. However, bizarrely, the dramatic irony that makes us know that it is him all along that he is looking for casts Oedipus in this play as a detective who is hunting for himself, and gradually pieces together the hideous truth. He certainly spares no efforts in his quest for truth, as is shown by the thorough and vigorous interrogation that he gives Creon. He even goes as far as to ask for the advice and wisdom of Teiresias in his quest. He says, at many stages, that he wants any scrap of information that could help him find the killer. Yet what is fascinating to focus on throughout the play is that the vibrant and defiant certainty that Oedipus has that the revelation of the truth will lead to the end of the punishment of Thebes is always contrasted to the severe reluctance of other characters to share and reveal their knowledge. It is clear that this reluctance is based on fear, as these characters are able to see what Oedipus is blind to until later on in the play - that their clues implicate Oedipus in the murder of Laius and point towards his involvement in the plague. Oedipus, for most of the play, remains ignorant, but as he gradually pieces together the clues he is given he makes the ultimate and desperate discovery of the truth, and his identity. Ironically, by his insistence that others reveal their information he is forced to confront ever-more his own role in this saga and how he has committed the unforgivable crime of patricide and incest. It is this final act of "seeing" himself for who he really is and knowing himself for whom he really is that ironically results in his own self-mutilation - he cannot bear to "see" any more in this life.
I have included a link to the enotes section of this play based on themes to help you investigate other themes.