The nature of the much debated valence state of an interstitial oxygen atom in oxygen-doped La2CuO4 is the subject of this paper. In model cluster calculations, we studied the position, charge, and spin state of the interstitial oxygen atoms in this superconductor. The models considered allow the interstitial oxygen to move off a symmetrical position, to have varying spin and charge, and to be surrounded by various magnetic environments. UB3LYP calculations show that a model having an interstitial oxygen atom with a total spin of I is lowest in energy; the interstitial oxygen atoms here act as stable radicals with a net charge of - 1. These results agree with experimental evidence for the paramagnetic behavior for interstitial atoms. The energy associated with a spin flip at a Cu site in our models is lower if interstitial oxygen has a local electron spin density, compared to the case when it does not. We provide a possible explanation for the increase of the doping concentrations of interstitial oxygen with a decrease of the Neel temperature of this system. The relative stability of the models we consider depends on their spin states, accompanied by structural changes; this explains indirectly the experimental change of the slope (from 2 to 1.3) of the linear relationship between the hole concentration and the oxygen content. Our results support a stripe phase in high temperature superconductivity; in our calculations, hole doping to the copper oxide layer comes only through the formation of an oxygen interstitial pair, not from any change of the local structural environment and magnetic field around the single interstitial.