We present evaluations of the interaction of neutrons with energies between 20 and 100 MeV with oxygen and nitrogen nuclei, which follows from our previous work on carbon. Our aim is to accurately represent integrated cross sections, inclusive emission spectra, and kerma factors, in a data library that can be used in radiation transport calculations. We apply the Feshbach-Kerman-Koonin-GNASH nuclear model code, which includes Hauser-Feshbach, pre-equilibrium, and direct reaction mechanisms, and use experimental measurements to optimize the calculations. We determine total, elastic, and nonelastic cross sections; angle-energy-correlated emission spectra for light ejectiles with A ≤ 4 and gamma rays; and average energy depositions. Our results for charged-particle emission spectra agree well with measurements of Subramanian et al. We compare kerma factors derived from our evaluated cross sections with experimental data, providing an integral benchmarking of our work.