Multilayer MoS2 possesses highly anisotropic thermal conductivities along in-plane and cross-plane directions that could hamper heat dissipation in electronics. With about 9% cross-plane compressive strain created by hydrostatic pressure in a diamond anvil cell, we observed about 12 times increase in the cross-plane thermal conductivity of multilayer MoS2. Our experimental and theoretical studies reveal that this drastic change arises from the greatly strengthened interlayer interaction and heavily modified phonon dispersions along cross-plane direction, with negligible contribution from electronic thermal conductivity, despite its enhancement of 4 orders of magnitude. The anisotropic thermal conductivity in the multilayer MoS2 at ambient environment becomes almost isotropic under highly compressive strain, effectively transitioning from 2D to 3D heat dissipation. This strain tuning approach also makes possible parallel tuning of structural, thermal and electrical properties, and can be extended to the whole family of 2D Van der Waals solids, down to two layer systems.