The point of view is dialogue so there is not a specific point of view. The characters are speaking to each other and there is no narration. The reliability of each character varies depending on the person. Oedipus does not seem very reliable at this point. I am not sure what to believe, of what he says and what to believe from what is said by other characters. The Profit seems more reliable to me now that the King confessed to killing the previous King. I am still a little uneasy about the profit but he is definately more reliable then the King.
Throughout the tragety the reader gets a really good idea and insight on each character. This is done by the strong personalities that are portrayed through the characters' dialogue. The reader is able to identify who to trust, who not to trust, who they like, who they don't like, ect.
The King and the Profit are probably the least credible of people in the tragety so far. The Profit is said to have lied in the past so there is no garuanttee that he is completely reliable and credible. The King is even less credible, he is mixed in a web of his own lies. The reader is now unable to identify whether he is lying or not any more.
The writer presents each character a certain way. For instance, the writer presents the character of Jocasta as the peace keeper of the land. This person is portrayed as a kind, magestic, sweet person through their dialogue. On the other hand King Oedipus is portrayed as a liar that cannot be trusted. The writer has this character go back and forth between lies and truths, in order to break the trust between this character and the reader. Many other characters are portrayed as either bad and cannot be trusted or good and very trustworthy. This is accomplished by the writer stirring up lies and gossip within the story. The reader can be thrown off by lies and such, but there is always either an ability to love or hate each character from this play.