Phase separation into a ferromagnetic (FM) metallic and a charge-ordered (CO) insulating state as found in the manganite (Pr1-yLay)(0.7)Ca0.3MnO3 (PLCMO) is expected to be sensitive to structural changes. Reversible biaxial strain has been applied to epitaxially grown films on piezoelectric substrates of (PbMg1/3Nb2/3O3)(0.72)(PbTiO3)(0.28) (001). Reversible strain experiments give a unique insight into the effect of strain on the magnetization and the electrical resistance, i.e., the so-called elastoresistance, of the films. 100-nm-thick PLCMO films of various Pr/La ratios have been grown using alternating pulsed laser deposition from a La-based and a Pr-based target. We have found a drastic reduction in the resistance, or a "colossal" elastoresistance, upon piezoelectrically controlled release of the tensile strain in the films, characterized by a resistive gauge factor of up to 1800. This result is qualitatively consistent with the magnetic measurements, where a higher saturation magnetization and an increased magnetic transition temperature are observed with the release of tensile strain. The elastoresistance is highest at chemical composition y approximate to 0.6, the metal-insulator phase boundary, and near the metal-insulator transition temperature, where the competition between the FM and CO ground states is strongest. This indicates that the coexistence of the FM and CO phases is strongly affected by strain with tensile strain suppressing the FM metallic phase.