This work presents results of time-resolved, absolute measurements of OH number density, nitrogen vibrational temperature, and translational-rotational temperature in air and lean hydrogen-air mixtures excited by a diffuse filament nanosecond pulse discharge, at a pressure of 100 Torr and high specific energy loading. The main objective of these measurements is to study kinetics of OH radicals at the conditions of strong vibrational excitation of nitrogen, below autoignition temperature. N-2 vibrational temperature and gas temperature in the discharge and the afterglow are measured by ns broadband coherent anti-Stokes Raman scattering. Hydroxyl radical number density is measured by laser induced fluorescence, calibrated by Rayleigh scattering. The results show that the discharge generates strong vibrational nonequilibrium in air and H-2-air mixtures for delay times after the discharge pulse of up to similar to 1 ms, with a peak vibrational temperature of T-v approximate to 1900 K at T approximate to 500 K. Nitrogen vibrational temperature peaks at 100-200 mu s after the discharge pulse, before decreasing due to vibrational-translational relaxation by O atoms (on the time scale of several hundred mu s) and diffusion (on ms time scale). OH number density increases gradually after the discharge pulse, peaking at t similar to 100-300 mu s and decaying on a longer time scale, until t similar to 1 ms. Both OH rise time and decay time decrease as H-2 fraction in the mixture is increased from 1% to 5%. Comparison of the experimental data with kinetic modeling predictions shows that OH kinetics is controlled primarily by reactions of H-2 and O-2 with O and H atoms generated during the discharge. At the present conditions, OH number density is not affected by N-2 vibrational excitation directly, i.e. via vibrational energy transfer to HO2. The effect of a reaction between vibrationally excited H-2 and O atoms on OH kinetics is also shown to be insignificant. As the discharge pulse coupled energy is increased, the model predicts transient OH number density overshoot due to the temperature rise caused by N-2 vibrational relaxation by O atoms, which may well be a dominant effect in discharges with specific energy loading.