The electron-hole exchange interaction is a fundamental mechanism that drives valley depolarization via intervalley exciton hopping in semiconductor multivalley systems. Here, we report polarization-resolved photoluminescence spectroscopy of neutral excitons and negatively charged trions in monolayer MoSe2 and WSe2 under biaxial strain. We observe a marked enhancement (reduction) on the WSe2 triplet trion valley polarization with compressive (tensile) strain while the trion in MoSe2 is unaffected. The origin of this effect is shown to be a strain-dependent tuning of the electron-hole exchange interaction. A combined analysis of the strain-dependent polarization degree using ab initio calculations and rate equations shows that strain affects intervalley scattering beyond what is expected from strain-dependent band-gap modulations. The results evidence how strain can be used to tune valley physics in energetically degenerate multivalley systems.