Layered thin films of the ferroelectric perovskite Ba0.85Ca0.15Ti0.9Zr0.1O3 (BCZT) and the ferromagnetic half-metal La0.80Sr0.20MnO3 (LSMO) are well-known multiferroic systems that show promise for spintronic applications. In this work, the structure–property relationships are explored in novel BCZT/LSMO thin film heterostructures with optimized ferroic properties. Epitaxial BCZT/LSMO thin film heterostructures are grown by varying the lattice mismatch strains on single crystal LaAlO3 (LAO) (100) and MgO (100) substrates using the pulsed laser deposition technique. The epitaxial strain in the films gives rise to a tetragonal distortion of the BCZT and LSMO unit cells and significantly affects their magnetotransport and magnetodielectric properties. The BCZT/LSMO/LAO heterostructure exhibits a colossal magnetoresistance effect due to a large out-of-plane tensile strain, which induces enhanced carrier hopping in the LSMO layer as compared to the BCZT/LSMO/MgO film. The larger tetragonal distortion of the BCZT unit cell in BCZT/LSMO/MgO contributes to higher dielectric permittivity, with a greater dielectric maxima temperature and freezing temperature. Magnetodielectric measurements reveal a hitherto unobserved giant magnetodielectric effect in the BCZT/LSMO/MgO film, attributed to a large in-plane strain, which induces interfacial polarization distortion at the interfacial layer. Overall, this work elucidates the unique strain and charge-mediated cross-coupled phenomena of magnetic and electric orders in multiferroic thin film heterostructures, which are critical for their technological applications.