Dynamic second-order nonlinear susceptibilities, $chi^{(2)}(2omega,omega,omega)equiv chi^{(2)}(omega)$, are calculated here within a fully first-principles scheme for monolayered molybdenum dichalcogenides, $2H$-MoX$_2$ (X=S,Se,Te). The absolute values of $chi^{(2)}(omega)$ across the three chalcogens critically depend on the band gap energies upon uniform strain, yielding the highest $chi^{(2)}(0)sim$ 140 pm/V for MoTe$_2$ in the static limit. Under this uniform in-plane stress, $2H$-MoX$_2$ can undergo direct-to-indirect transition of band gaps, which in turn substantially affects $chi^{(2)}(omega)$. The tunability of $chi^{(2)}(omega)$ by either compressive or tensile strain is demonstrated especially for two important experimental wavelengths, 1064 nm and 800 nm, where resonantly enhanced non-linear effects can be exploited: $chi^{(2)}$ of MoSe$_2$ and MoTe$_2$ approach $sim$800 pm/V with -2% strain at 1064 nm.
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