We have fabricated magnetoelectric heterostructures by growing ferromagnetic La1-xBaxMnO3 (x=0.2, 0.4) thin films on (001)-, (110)-, and (111)-oriented 0.31Pb(In1/2Nb1/2)O3-0.35Pb(Mg1/3 Nb1/2)O3-0.34PbTiO3 (PINT) ferroelectric single-crystal substrates. Upon poling along the [001], [110], or [111] crystal direction, the electric-field-induced non-180° domain switching gives rise to a decrease in the resistance and an enhancement of the metal-to-insulator transition temperature TC of the films. By taking advantage of the 180° ferroelectric domain switching, we identify that such changes in the resistance and TC are caused by domain switching-induced strain but not domain switching-induced accumulation or depletion of charge carriers at the interface. Further, we found that the domain switching-induced strain effects can be efficiently controlled by a magnetic field, mediated by the electronic phase separation. Moreover, we determined the evolution of the strength of the electronic phase separation against temperature and magnetic field by recording the straintunability of the resistance [(ΔR/R)strain] under magnetic fields. Additionally, opposing effects of domain switching-induced strain on ferromagnetism above and below 197K for the La0.8Ba0.2MnO3 film and 150K for the La0.6Ba0.4MnO3 film, respectively, were observed and explained by the magnetoelastic effect through adjusting the magnetic anisotropy. Finally, using the reversible ferroelastic domain switching of the PINT, we realized non-volatile resistance switching of the films at room temperature, implying potential applications of the magnetoelectric heterostructure in non-volatile memory devices. [ABSTRACT FROM AUTHOR]