Good question. You often read about people whose Oscar/s have gone off their food and haven't eaten for well over a week. So that is the case, an Oscar isn't going to starve to death after the first week. Whereas I wouldn't recommend leaving a young Oscar for too long without food, I think he will be okay for a week. Fish can actually go for a few weeks without food.
I've not seen any suitable auto feeders for Oscars, they are normally made for very small community fish. Leaving food in the tank is not a good idea, that will just increase the chances of poor water quality.
Don't worry too much, most living creatures can go without food for a week easily, fish are no different. Just give them a good meal just before you go.
Just make sure he's got plenty to drink