Temperature-programmed desorption (TPD) and reflection-absorption infrared spectroscopy (RAIRS) are used to probe the effect of atomic and molecular oxygen (O and O2) beams on amorphous silica (aSiO2) and water (H2O) surfaces (porous-amorphous solid water; p-ASW, compact amorphous solid water; c-ASW, and crystalline solid water; CSW). Altering the deposition method of O2 is shown to result in different desorption energies of O2 due to differences in O2 film morphology when deposited on the aSiO2 surface. O2 enthalpy of formation is dissipated into the aSiO2 substrate without changes in the silica network. However, on the H2O surfaces, O2 formation enthalpy release is dissipated into the H-bonded matrix leading to morphological changes, possibly compacting p-ASW into c-ASW while CSW appears to undergo amorphisation. The enthalpy release from O2 formation is, however, not enough to result in reactive desorption of O2 or H2O under the current experimental circumstances. Further to this, O2 formation on sub-monolayer quantities of H2O leads to enhanced de-wetting and a greater degree of H-bond reconnection in H2O agglomerates. Lastly, O3 is observed from the O + O2 reaction on all surfaces studied.