You must be joking! I spent 3 weeks there this past May, nothing happened to me, I had the absolute wonderful time! I felt really safe, no one tried to attack me. I know quite a few people who travel to Odessa and I have never heard them complaining of their safety, infact.. they all say how beautiful and friendly Odessa is! You must be getting your info from "Paranoid Anonimous"... Police is definately corrupted in Ukraine, Turkey...etc.. and you should be very cautious when dealing with them, but to stay away from a city because you're scared is ridiculous.
If you are a generally paranoid and foolish person, you should not travel at all, every city and country has it's problems, you just have to be smart and look out for yourself everywhere you go, even or especially in U.S.
Good Luck!