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This paper comprehensively investigates the oblique propagation of ion-acoustic solitary waves (IASWs) with arbitrary amplitude in a magnetoplasma consisting of inertialess non-Maxwellian (nonthermal) electrons, inertialess Maxwellian positrons, and inertial adiabatically heated ions. It is postulated that the positive ions demonstrate adiabatic behavior that is distinguished by anisotropic thermal pressure. The study utilizes Sagdeev's pseudopotential theory to analyze the fluid equations of the plasma model and reduce them to the energy equation. Different plasma configuration factors, such as nonthermal parameters, positron concentration, and parallel and perpendicular ion pressure, are being studied to see how they affect the properties of solitary waves with large amplitudes. The findings demonstrate the simultaneous coexistence of compressive and rarefactive IASWs, significantly influenced by positrons and nonthermal electron parameters. The study provides valuable insights into wave phenomena in magnetized plasmas and presents possible applications in both Space and laboratory plasma environments. [ABSTRACT FROM AUTHOR]