What is the most compact way to store Oxygen? Perhaps I should qualify that as being at room temperature since the most compact form of oxygen is probably liquid oxygen. At room temperature would it be better to store it as rust or compressed air or something else, like hydrogen peroxide?
Solid ozone has a density of 1.728 g/cm3 according to The Density of Solid Ozone J. Am. Chem. Soc., 1959, 81, pp 805–806.
Best I can think of at atmospheric pressure, assuming your goal is to store and recover as much pure oxygen as possible in a given volume.
If your goal is just to pack as many oxygen atoms in a given volume, BeO, which has a density of 3.01 g/cm3 is better.
At high pressure there is metallic oxygen.