Properties of the α and β phases of solid O2 are calculated with a deformable-cell Monte Carlo method and the character of the associated phase transition is delineated. We find that the monoclinic α phase is stable at temperatures T≲18 K and in- and out-of-plane antiferromagnetic order is predicted that is in accord with experiment. The magnetic correlations appear to be long ranged. A phase transition into β-O2 occurs at T=17.75±0.2 K. It is first order with a calculated volume change ΔV=0.06±0.10 cm3/mole, and is accompanied by a magnetic transition into a highly dynamic quasihelical state with a correlation length lc=8±1 Å at 18 K, that decreases rapidly with increasing temperature. The results indicate that O2 behaves as a two-dimensional magnetic system. The molecular axes exhibit temperature dependent, small angle libration about an axis normal to the basal plane and there is no evidence of precession in β-O2. There is also no evidence of magnetic reordering in the α phase as a precursor to the transition.