Water and oxygen molecules determine many of the properties of amorphous SiO2 used in several technologies, but the underlying atomic-scale processes remain unresolved. We report results of first-principles calculations showing that a wide range of behavior is possible in an amorphous environment, including diffusion of the molecule as a whole and various reactions with the network. Experimental data including oxygen exchange reaction and radiation sensitivity are accounted for. The possibility of H3O+ formation as a source of positive charge is discussed.