What you are trying to achieve is enough room for the fish to be able to turn around comfortably. For a single oscar a 48"x18" aquarium is suffcient, but in reality you want them to have a little more room to turn than that. That gets back to being in a box, you could turn around, but barely and I doubt you would be comfortable. Granted height is not an issue. My fish do tend to swim at the top of the aquarium from time to time, but normally only to beg for food or to see what I am doing. ideally you want to get as big of a tank as you can afford. Smaller tanks breed aggression. The bigger the tank you have the more fish you can have. I would love to have a 10,000 gallon tank, but my wife would tell me to go live in it if I brought one home, .
If the 20 gallon is all you have at the time and the fish is "healthy" and you dont have the money to buy proper home for him, then I would suggest that you try to find a better home for him. Many lfs will take adult fish off your hands, but dont expect a lot of $ for him. A convict would be better suited for your tank and provide almost as much personality as an oscar.
Just remember its all about the fish.