The effect of external strain on the evolution of magnetic multi-vortices in nanoscale ferromagnetic platelets is investigated by a phase field model that explicitly includes the coupling between the magnetization and deformation. Phase field simulations show that a compressive strain makes the magnetic vortex-antivortex pair stable in rectangular ferromagnetic platelets, which is unstable in the absence of an external magnetic field and strain. The magnetic clockwise (CW) and counterclockwise (CCW) vortex pairs disappear in ferromagnetic platelets under an external magnetic field through the annihilation of the vortex and antivortex, or through expulsion when external strain is absent. In the presence of tensile strain, the expulsion of CW and CCW vortices is suppressed in ferromagnetic platelets. However, external strain has less effect on the annihilation of CW and CCW vortices. For ferromagnetic platelets with triple vortices, both tensile strain and a magnetic field induce the annihilation and expulsion of vortices. The effect of strain on the evolution of magnetic vortices suggests a new way to control them by strain engineering.