The structural, magnetic, magnetocaloric and Griffiths phase (GP) disorder of non-stoichiometric perovskite manganites La0.8−xSr0.2−yMn1+x+yO3 are reported here. Determination of valence states and structural phases evidenced that the smaller cations Mn2+ and Mn3+ will not occupy the A-site of a perovskite under atmospheric synthesis conditions. The same analysis also supports that the vacancy in the A-site of a perovskite induces a similar vacancy in the B-site. The La3+ and Sr2+ cation substitutions in the A-site with vacancy influences the magnetic phase transition temperature (TC) inversely, which is explained in terms of the electronic bandwidth change. An anomalous non-linear change of the GP has been observed in the Sr-substituted compounds. The agglomeration of Mn3+-Mn4+ pairs (denoted as dimerons), into small ferromagnetic clusters, has been identified as the reason for the occurrence of the GP. A threshold limit of the dimeron formation explains the observed non-linear behaviour of the GP formation. The Sr-substituted compounds show a relatively large value of isothermal entropy change (maximum 3.27 J/kgK at μ0H=2T) owing to its sharp magnetic transition, while the broad change of magnetization in the La-substituted compound enhances the relative cooling power (maximum 98 J/kg at μ0H=2T).