We review the results of a wide range of nuclear magnetic resonance (NMR)measurements of the local order parameters and the molecular dynamics of solid ortho-para hydrogen mixtures and solid nitrogen-argon mixtures that form novel molecular orientational glass states at low temperatures. From the NMR measurements, the distribution of the order parameters can be deduced and, in terms of simple models, used to analyze the thermodynamic measurements of the heat capacities of these systems. In addition, studies of the dielectric susceptibilities of the nitrogen-argon mixtures are reviewed in terms of replica symmetry breaking analogous to that observed for spin glass states. It is shown that this wide set of experimental results is consistent with orientation or quadrupolar glass ordering of the orientational degrees of freedom.