Oedipus is seeking himself. All the people Oedipus seeks information from only have information about him. The stories he insists on hearing from Tiresias and the shepherd hinge on him and only him.
This is the irony of Oedipus being a "stranger to the story". He does not know the story, but it is his own story.
As he seeks the source of the plague on Thebes, he seeks himself. As he attempts to discover the murderer of the former king of Thebes, Laius, he discovers that he murdered the man, his father, on the road to Thebes.
...by demanding that others tell him all they know he is forced to confront the hideous facts of his patricide and incest.
He insists on his own innocence and good intentions, yet he can only be said to have good intentions, not innocence. When the truth of his own story comes home to Oedipus, he is overwhelmed. In the end he is no longer a stranger to his story, but he becomes a stranger to his family, blinding himself and leaving home to become a wanderer, punishing himself by binding himself to his story and severing himself from all else.