Ultra-thin epitaxial Ni-Mn-Ga films, 10-15 nm thick, were grown by magnetron sputtering on MgO(001), either directly on the substrate or on a Cr buffer, and studied by X-ray diffraction, magnetometry, and magneto-optical Kerr effect (MOKE) spectroscopy. The films were austenitic, with the cubic cell tetragonally distorted in opposite directions. The film on bare MgO was stretched in-plane (c/a=0.989) and the film on Cr was compressed in-plane (c/a=1.021), while their unit-cell volumes differed by less than 0.3%. As the thermal expansion mismatch was expected to stretch the films in-plane in both cases, the opposite distortions were attributed to the lattice misfit. The room-temperature magnetization loops of the two films did not show significant differences, but their polar and longitudinal MOKE spectra differed in the amplitude, sign, and energy of the spectral structures over the whole 0.76-5 eV range. Magneto-optical simulations showed that the absence of the Cr buffer accounted only for the stronger low-energy polar MOKE rotation extremum of the film on MgO. We attributed the other changes to the strain-induced change of the electronic structure, consistent with theoretical predictions in which the d_(x²-y²) and d_(3z²-r²) sub-bands of the minority-spin Ni e_g states exchange their order when the distortion changes sign. In parts of the spectrum, the two films showed Kerr rotation or ellipticity of opposite sign, so the choice of the growth template or a dynamically induced distortion can switch the sign of the magneto-optical response at a given photon energy.