Does pure oxygen and pure nitrogen have the same volume?

No. Oxygen and Nitrogen molecules are not the same size. China has a railroad that rides along at 20,000 feet in Tibet. They pump air into the cars. The cars have filters. Nitrogen gas leaves through the filters and oxygen remains in the railroad cars. By using simple pumps and filters they increase the amount of oxygen in the cars. If oxygen and nitrogen were the same size, it would not work.