Synthetic ferrimagnets are an attractive material class for spintronics as they provide access to all-optical switching of magnetization and, at the same time, allow for ultrafast domain wall motion at angular momentum compensation. In this work, we systematically study the effects of strain on the perpendicular magnetic anisotropy and magnetization compensation of Co/Gd and Co/Gd/Co/Gd synthetic ferrimagnets. First, the spin reorientation transition of a bilayer system is investigated in wedge type samples, where we report an increase in the perpendicular magnetic anisotropy in the presence of in-plane strain. Using a model for magnetostatics and spin reorientation transition in this type of system, we confirm that the observed changes in anisotropy field are mainly due to the Co magnetoelastic anisotropy. Second, the magnetization compensation of a quadlayer is studied. We find that magnetization compensation of this synthetic ferrimagnetic system is not altered by external strain. This confirms the resilience of this material system against strain that may be induced during the integration process, making Co/Gd ferrimagnets suitable candidates for spintronics applications.