We propose a unique strategy to apply stronger strain at heterointerfaces than conventional epitaxial strain methods to extract hidden attractive physical/chemical properties in materials. This strategy involves precisely accounting for the epitaxial strain induced by lattice mismatch as well as the differences in the thermal expansion coefficients and compressibilities of epitaxial films and substrates. We selected optimally cobalt-doped BaFe2As2(Ba122:Co), an iron-based superconductor with a bulk critical temperature (Tc) of 22 K, as a model material and four types of single-crystal substrates. Ba122:Co was selected because its Tc is robust to hydrostatic pressure but sensitive to epitaxial strain (i.e., one of the anisotropic strains), and the selected substrates entirely cover the positive/negative lattice mismatches, thermal expansion coefficients, and compressibilities with respect to Ba122:Co. With strong anisotropic strain successfully induced by film growth, external hydrostatic pressurizing, and cooling processes, we observed unique carrier transport properties in Ba122:Co epitaxial films on CaF2 and BaF2 substrates including (i) upturn behavior in the temperature dependence of the longitudinal resistivity, (ii) negative magnetoresistance, (iii) large enhancement of anomalous Hall effects in the epitaxial films on CaF2, and (iv) enhancement of Tc to 27 K in the epitaxial films on BaF2. These results demonstrate the effectiveness of our strategy, and this approach can be further extended to other inorganic materials in thin-film form.