What is the most compact way to store Oxygen?
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.