This kind of behaviour is not uncommon if you have various Oscar's living together. I must ask you come at how big is your tank? You need a fairly big tank for four Oscars. If you try and squeeze a few Oscars into a small tank then you are asking for trouble. I'm afraid there isn't really any advice I can give you that will stop your Oscar from picking on the others. The best thing you can do is re-home some fish.
As for the injuries, depends how big they are, if the Oscar has actually lost its lip then it will not grow back, it will probably be disfigured. However, as long as it's not too bad, it should manage to eat okay.