In the play Oedipus is searching for Laius' murderer because an oracle tells him only when the murderer is punished will a plague end, but at the end we learn that he is the murderer. So that makes him a criminal and a detective.
The theme of 'Dragonwings' is change. People are usually worried about change, but the change most likely will have a positibe outcome, which is what happens with Moon Shadow and his family. The setting in the book first took place in China, which was Moon Shadow's first home.