Rare earth oxyhydrides REOxH(3-2x), with RE = Y, Sc, or Gd and a cationic FCC lattice, are reversibly photochromic in nature. It is known that structural details and anion (O2-:H-) composition dictate the efficiency of the photochromic behavior. The mechanism behind the photochromism is, however, not yet understood. In this study, we use 1H, 2H, 17O, and 89Y solid-state NMR spectroscopy and density functional theory (DFT) calculations to study the various yttrium, hydrogen, and oxygen local environments, anion oxidation states, and hydride ion dynamics. DFT models of YOxH(3-2x) with both anion-ordered and anion-disordered sublattices are constructed for a range of compositions and show a good correlation with the experimental NMR parameters. Two-dimensional 17O-1H and 89Y-1H NMR correlation experiments reveal heterogeneities in the samples, which appear to consist of hydride-rich (x ≈ 0.25) and hydride-poor domains (x ≈ 1) rather than a single composition with homogeneous anion mixing. The compositional variation (as indicated by the different x values in YOxH(3-2x)) is determined by comparing static 1H NMR line widths with calculated 1H-1H dipolar couplings of yttrium oxyhydride models. The 1D 17O MAS spectrum demonstrates the presence of a small percentage of hydroxide (OH-) ions. DFT modeling indicates a reaction between the protons of hydroxides and hydrides to form molecular hydrogen (H+ + H- → H2). 1H MAS NMR indicates the presence of a mobile component that, based on this finding, is attributed to trapped molecular H2 in the lattice.