Some people may think I'm all wet, but I believe a 75 gal tank is too small for an oscar over 7.5". So if you put it in a 75, with normal growth, you will need another larger tank in about a month or so.
I agree with tlindsey, you will need to move the old filter to the 75 and keep it running until the new tank cycles.
That is, unless the filter and substrate laden with the pathogenic bacteria that are making the oscar sick, as a result of being kept too small tank.
Would you keep a normal size dog in a tiny bathroom 24/7 ?