Multiple, consecutive high-temperature transitions in NaI involving dynamical order and/or localization in the energy-momentum spectrum but not in the average crystal structure are revealed by lattice dynamics, x-ray lattice spacing, and heat-capacity measurements. Distinctive energy-momentum patterns and lattice distortions indicate dynamical structures forming within randomly stacked planes, rather than the isolated point-defect-like intrinsic localized modes predicted. Transition entropies are accounted for by vibrational entropy changes, and the transition enthalpies are explained by the strain energy of forming stacking-fault-like planar distortions deduced from x-ray-diffraction peak shifts. The vibrational entropy of the dynamical structures stabilizes surrounding elastic distortions.