Homogeneous in-plane biaxial tensile strain strengthens the out-of-plane van der Waals (vdW) interaction in MoS bilayers (BLs) and can be used to fine-tune their terahertz (THz) oscillations. Using ultralow-frequency Raman spectroscopy on hexagonal (2H) and rhombohedral (2R) stacked BLs, we observe a hardening of the interlayer breathing modes originating from a strain-induced Poisson contraction of the vdW separation between the layers characterized by an effective out-of-plane Poisson's ratio of νeff ≈ 0.19--0.24. Strikingly, this geometric contraction drives the system into a highly repulsive regime of the intermolecular potential, corresponding to a Grüneisen parameter of γ ≈ 14--20. This value surpasses even the `giant' one reported for phosphorene, establishing these van der Waals BLs as highly tunable nonlinear mechanical platforms that can be addressed at the THz regime without external pressure knobs.