Hi It is their nature to be territorial and often this means fighting.
It is a crap shoot with Oscars, trying to find ones that can live peacefully together. There is no recipe for success, such as 'males + females are fine..Females + females are fine..older + younger is fine' etc. etc. Male or female, young or old, any Oscar can potentially be very aggressive with any other Oscar.
If you see that they are causing injury to each other it might be time to separate. It is normal for them to engage in somewhat rough looking behavior, that is how they are. But when you start to see injuries, it will likely get worse over time.
You can try re-arranging the decor, with decor (rocks, plants, driftwood etc) on each end of the tank and less decor in the center so this area is less likely to be 'claimed' and to interrupt their sight line to each other... but I can tell you of my experiences trying to placate Oscars that have decided they dont want to share territory, that once the line has been drawn the only thing I was able to do was separate them.
It is almost impossible to visually sex Oscars, and if you happen to have 2 males there is not much you can do to stop the fighting.
I have not had a Green Terror or Parrot, but I know they can also be very territorial (hence the name 'Terror').
Right now I have my most territorial Oscar in his very own 100 gallon tank, my 2 that are good buddies in their own 130 gallon tank and 2 adorable babies that for now are in my 55 with little guys (Cory's etc). When they are older we will see how they feel about each other and move them to appropriate tanks accordingly, lol...
I hope it works out with your Oscars. That is a beautiful tank!
