We have performed a detailed and comprehensive analysis of the dynamics of water molecules and hydronium ions in hydrated Nafion using classical molecular dynamics simulations with the DREIDING force field. In addition to calculating diffusion coefficients as a function of hydration level, we have also determined mean residence time of H2O molecules and H3O+ ions in the first solvation shell of SO3- groups. The diffusion coefficient of H2O molecules increases with increasing hydration level and is in good agreement with experiment. The mean residence time of H2O molecules decreases with increasing membrane hydration from 1 ns at a low hydration level to 75 ps at the highest hydration level studied. These dynamical changes are related to the changes in membrane nanostructure reported in the first part of this work. Our results provide insights into slow proton dynamics observed in neutron scattering experiments and are consistent with the Gebel model of Nafion structure.