Ceramic samples of lanthanum strontium manganite perovskites La0.6Sr0.2Mn1.2 − xNixO3 ± δ (0 ≤ x ≤ 0.3) have been investigated using the X-ray diffraction, magnetic (χac), 55Mn NMR, resistive, and magnetoresistive methods. The specific features of the influence of the composition on the structure and properties of nonstoichiometric manganite perovskites have been established. It has been found that the rhombohedrally (R\(\bar 3\)c) distorted perovskite structure contains cation and anion vacancies, as well as nanostructured clusters with Mn2+ ions in the A-positions. The substitution of Ni3+ ions (r = 0.74 A) for Mn3+ ions (r = 0.785 A) leads to a decrease in the lattice parameter a, the ferromagnetic-paramagnetic phase transition temperature TC, and the metal-semiconductor phase transition temperature Tms due to the disturbance of the superexchange interactions between heterovalent manganese ions Mn3+ and Mn4+. The observed anomalous magnetic hysteresis at 77 K has been explained by the antiferromagnetic effect of the unidirectional exchange anisotropy of the ferromagnetic matrix structure on the magnetic moments of the superstoichiometric manganese Mn2+ ions located in nanostructured planar clusters. An analysis of the asymmetrically broadened 55Mn NMR spectra of the compounds has revealed a high-frequency electronic superexchange of the ions Mn3+ ⟷ O2− ⟷ Mn4+; a local heterogeneity of their surrounding by other ions, vacancies, and clusters; and a partial localization of Mn4+ ions. The local hyperfine interaction fields on 55Mn nuclei have been determined. The concentration dependences of the activation energy and charge hopping frequency have confirmed that the Ni ions decrease the electrical conductivity due to the weakening of the electronic superexchange Mn3+ ⟷ O2− ⟷ Mn4+. Two types of magnetoresistive effects have been found: one effect, which is observed near the phase transition temperatures TC and Tms, is caused by scattering at intracrystalline nanostructured heterogeneities, and the other effect, which is observed in the low-temperature range, is induced by tunneling through intercrystalline mesostructured boundaries. The phase diagram has demonstrated that there is a strong correlation between magnetic and electrical properties in rare-earth manganites.