Motivated by the prospect of strain control of terahertz (THz) magnons, we have used resonant x-ray diffraction and Raman scattering to investigate the magnetic ground state and excitations of the layered Mott insulator Ca${}_2$RuO${}_4$ under uniaxial strain. We discovered a strain-induced phase transition between two antiferromagnetic states that differ in the sign of the interlayer exchange interaction. Although this interaction is weak and partially frustrated, the corresponding magnon energies of the two states differ by more than 10% ($\sim$ 0.3 THz). Our theoretical analysis explains this surprising observation by tracing the origin of both the sign reversal of the interlayer coupling and the magnon energy to the spin-orbital composition of the Ru valence electrons. The extreme strain sensitivity of the THz magnon energy near a magnetic phase transition opens up pathways towards a new generation of "transition-edge" magnonic devices.