Not a LEO, but I'm pretty much on the same boat as you. Over the past year I've taken 5 oral interviews with the last 4 passing. For the first interview I was quite nervous and didn't know what to expect. Usually the interview consists of brief introductory questions such as "How have you prepared for this position?" and "Why do you want to become a police officer"? etc. Those type of questions you can prepare for. The next series of questions will be scenario based ones which will test your intelligence, quick thinking, judgement and common sense. These can range from integrity type scenarios to shoot or no shoot situations. Out of the 5 oral boards I tested with, none of the scenarios were the same. Some were similar but never the same. I suggest lurking on Law Enforcement Forums where they have a thread all about oral interviews. Some advice for the oral interview is try to be calm and fully listen to the question before responding. Try to formulate what you want to say before you start speaking. Worst thing can happen is you start rambling off on a question and have no idea where its taking you.
I'm in backgrounds with a couple of agencies and mainly the background check is verifying everything you put down for your PHS (Personal History Statement). The PHS consists of everything about your life such as every place you lived, schools you attended to every job you held. Of course they do a criminal background check on you and they also want to know what kind of friends you have, if you ever associated yourself with gangs etc.
Good luck to you!