Dynamical strain generated upon excitation of a metallic film by a femtosecond laser pulse may become a versatile tool enabling control of magnetic state of thin films and nanostructures via inverse magnetostriction on a picosecond time scale. Here we explore two alternative approaches to manipulate magnetocrystalline anisotropy and excite magnetization precession in a low-symmetry film of a magnetic metallic alloy galfenol (Fe,Ga) either by injecting picosecond strain pulse into it from a substrate or by generating dynamical strain of complex temporal profile in the film directly. In the former case we realize ultrafast excitation of magnetization dynamics solely by strain pulses. In the latter case optically-generated strain emerged abruptly in the film modifies its magnetocrystalline anisotropy, competing with heat-induced change of anisotropy parameters. We demonstrate that the optically-generated strain remains efficient for launching magnetization precession, when the heat-induced changes of anisotropy parameters do not trigger the precession anymore. We emphasize that in both approaches the ultrafast change of magnetic anisotropy mediating the precession excitation relies on mixed, compressive and shear, character of the dynamical strain, which emerges due to low-symmetry of the metallic film under study.