Strain is a powerful experimental tool to explore new electronic states and understand unconventional superconductivity. Here, we investigate the effect of uniaxial strain on the nematic and superconducting phase of single crystal FeSe using magnetotransport measurements. We find that the resistivity response to the strain is strongly temperature dependent and it correlates with the sign change in the Hall coefficient being driven by scattering, coupling with the lattice and multiband phenomena. Band structure calculations suggest that under strain the electron pockets develop a large in-plane anisotropy as compared with the hole pocket. Magnetotransport studies at low temperatures indicate that the mobility of the dominant carriers increases with tensile strain. Close to the critical temperature, all resistivity curves at constant strain cross in a single point, indicating a universal critical exponent linked to a strain-induced phase transition. Our results indicate that the superconducting state is enhanced under compressive strain and suppressed under tensile strain, in agreement with the trends observed in FeSe thin films and overdoped pnictides, whereas the nematic phase seems to be affected in the opposite way by the uniaxial strain. By comparing the enhanced superconductivity under strain of different systems, our results suggest that strain on its own cannot account for the enhanced high $T_c$ superconductivity of FeSe systems.