Structure and reaction dynamics in solid H-2/D-2 doped with O(P-3, D-1, S-1) is investigated through simulations based on accurate ab initio potential energy surfaces. The ab initio calculations are performed at MCSCF level, with neglect of spin-orbit interactions. The dynamical simulations rely on nonadditive effective potentials, taking into account the anisotropy of the open shell atom by using diabatic representations for the globally fitted potential energy surfaces of O-H-2. The ground state of the doped solid is well described as O(P-3) isolated in para-H-2(J=0) since the atom-molecule interaction anisotropy is not sufficient to orient H-2. O(P-3) atoms radially localize the nearest-neighbor shell, and lead to a linear increase in the density of the solid as a function of impurity concentration. The doped solid is stable at cryogenic temperatures, with a free energy barrier for recombination of next nearest-neighbor O(P-3) atoms of 120 K. The solid state O(D-1) + H-2 reaction is considered in some depth. While in high symmetry sites the reaction is forbidden, even at 4 K, thermal fluctuations are sufficient to promote the insertion reaction.