For me, it was reading P&P like you said and reading up on criminal and traffic statutes of my state along with other things they saw fit for us to read up on. I also had two oral boards, a Sgt.'s and a Chief's. I also had a "scenario" to do which was different to say the least. This was done for the Sgt. and Cpl. promotion. I didn't get promoted Sgt., but I did get Cpl. Also a lot of it was political. They will never say, but everyone in the process knew who was going to get Sgt., the one's left over got Cpl. Call it favoritism or whatever you want, it was wrong. I no longer work at that dept., moved on to bigger and better.
All I can tell you is to study what they said, tell them what they want to hear and do your best. We all know there is a difference in what you would actually do in a certain situation and what they think you would do in that situation. They know what the answer should be and have known for a while. You are going in to the unknown and have to react the best you can at that time, just like a real incident. They will be armchair quarterbacking your answer, like an attorney.
Having a study group also helps. Get together with others and find out what each other would do in certain situations. They may have a different way of studying that may benefit you. Ask lots of questions to officer's who have been promoted. Pick their brain. The only stupid question is the one that is not asked!
Good luck. Do your best and let us know the outcome.