We have investigated the effects of large static uniaxial strain, up to \ensuremath{\sim}3 GPa, on the excitons ${Z}_{1,2}$ and ${Z}_{3}$ of the cuprous halides using a gasketed diamond anvil cell. From the shifts and the stress-induced splittings of these excitons, we have obtained orbital and spin-orbit hydrostatic and shear deformation potentials. We have found that the shear deformation potential $d={d}_{1}+2{d}_{2}$ is positive for CuCl and negative for CuBr and CuI. Our measurements also show that the deformation potential of the spin-orbit splitting, $\frac{d{\ensuremath{\Delta}}_{0}}{d\mathrm{ln}V}$, is negative for all three copper halides. From the pressure dependence of the intensity ratio $\frac{{I}_{{Z}_{1,2}}}{{I}_{{Z}_{3}}}$ we have been able to obtain reliable values for the electron-hole exchange energy of the edge excitons in CuCl and CuBr.