Macroscopic thermodynamic and transport properties of disordered materials are determined largely by their local structure, which may differ substantially from long-range crystalline symmetry. In order to better understand local structure and ionic motion in highly disordered perovskite oxides, we have investigated several cubic perovskites using high-temperature oxygen-17 NMR in conjunction with other experimental techniques. Materials we have studied include Ba (In0.67Zr0.33)Oy, Ba(In0.67Ce0.33)Oy (La0.5Ba0.5) (Co0.7Cu0.3Oy, and (La0.6Sr0.4) (Co0.8Cu0.2)Oy. We show that despite having long-range cubic symmetry as determined by X-ray and neutron powder diffraction, these materials possess microdomains with layered structures on a short length scale (50-500 angstrom). These microdomains are apparent in HRTEM images of these materials, and manifest themselves as unit cell doublings in the electron diffraction patterns. Neutron powder profile refinements and oxygen-17 DAS NMR both suggest that oxygen nuclei are displaced from sites of cubic symmetry in a manner reminiscent of layered perovskite-related structures. As is the case with known layered materials, the high temperature oxygen-17 spectra and relaxation measurements show that few oxygen atoms are mobile below 800-degrees-C due to trapping of oxygen-ion vacancies in ordered layers. In the case of (La0.6Sr0.4)(Co0.8Cu0.2)Oy, estimates of the vacancy trapping energy and the vacancy migration energy, extracted from NMR, appear to rationalize macroscopic transport measurements.