Molecular dynamics simulations are carried out to compute the intradiffusion coefficients of H2 and O2 in H2O for temperatures ranging from 275.15 to 975.15 K and pressures ranging from 0.1 to 200 MPa. These conditions span vapor, liquid, and supercritical conditions. For the vast majority of the state points examined, experimental data are not available. The accuracy of six H2 and six O2 force fields is tested in reproducing the available experimentally measured densities, self-diffusivities, and shear viscosities of the pure gas and the intradiffusivity of the gas in H2O. Namely, we screen the H2 force fields developed by Buch, Vrabec and co-workers, Hirschfelder et al., Cracknell, a modified Silvera-Goldman, and Marx and Nielaba. For O2, the force fields by Bohn et al., Miyano, Coon et al., Hansen et al., Vrabec et al., and Watanabe are tested. Overall, the force fields by Buch and Bohn for H2 and O2, respectively, were found to perform the best, and combined with the TIP4P/2005 H2O force field are used to compute the intradiffusivities in the entire temperature and pressure range. The new data are used to develop an engineering model that can predict the H2 and O2 intradiffusivity in vapor, liquid, and supercritical H2O. The new model uses 11 parameters and has an accuracy of 4-11%. The model is validated with other available experimental and simulation data for H2 and O2 in H2O and pure H2O. Aside from the extensive collection of new data for the intradiffusivities of H2 and O2 in H2O, we present new data for the densities, shear viscosities, and self-diffusivities of pure TIP4P/2005 H2O in the same wide temperature and pressure range. The new data and the engineering model presented here can be used for the design and optimization of chemical processes, for which the knowledge of H2 and O2 diffusivities in H2O is important.