I think Paul wanted to show them that his life was a testament to the grace of God. He wanted to show them that even though he was a blasphemer and persecutor-two incredibly serious sins against God Himself-God's grace transcended that and Paul was shown truth and mercy. In order to do that, he starts with something they can relate to-the law. He decribes that the law is for the ungodly and sinful in order to show them the right way to act. Perhaps members of the church at Ephesus will see themselves in some of these descriptions.
Then Paul goes on to give them hope-he was once a sinner against God, but now with God's mercy Paul is His servant. He wants to create in them a hunger for truth, justice and God's love. I think he is doing this so that they will draw back to the important things of serving the church instead of being caught up in the false doctrines and controversies that are splitting them apart.