The better understanding of nanosecond scale discharges under atmospheric pressure and the validation of plasmachemical models, require an increasing need for reliable data. This paper presents, in the first time to our knowledge, spatiotemporal description of the gas number densities of major species including O atoms, the hydrodynamic expansion and the relative distribution of the energy deposited in the specific molecular modes of N-2(X) and O-2(X) following a nanosecond pulsed air discharge at atmospheric pressure. These data are obtained from phase-locked average profiles of the ground states of N-2 and O-2 probed by spontaneous Raman scattering. The results complete part I of this investigation dedicated to the gas temperature and the vibrational distribution function of N-2 and O-2 and show that half of the total energy deposited is loaded on the vibrational mode (48% for N-2 and 2% for O-2). The energy released into fast gas heating represents 19% of the energy deposited. This fast gas heating (up to 1000 K) observed in tens of nanoseconds after the current rise leads to a shock wave propagation shown with the pressure measurements. These processes combined with vibration-vibration/translation energy transfers and convective transports induced by the shock wave propagation are spatiotemporally studied. The experimental data of this study provide space and time database for the validation of plasmachemical models of nanosecond pulsed discharges in atmospheric pressure air.