We investigate how the dynamical state of molecular clouds relates to host galaxy environment and how this impacts the star formation efficiency (SFE) in the Milky Way and seven nearby galaxies. We compile measurements of molecular cloud and host galaxy properties, and determine mass-weighted mean cloud properties for entire galaxies and distinct subregions within. We find molecular clouds to be in ambient pressure-balanced virial equilibrium, where clouds in gas-rich, molecular-dominated, high-pressure regions are close to self-virialization, whereas clouds in gas-poor, atomic-dominated, low-pressure environments achieve a balance between their internal kinetic pressure and external pressure from the ambient medium. The SFE per free-fall time of molecular clouds is low, ∼0.1%-1%, and shows systematic variations of 2 dex as a function of the virial parameter and host galactic environment. The trend observed for clouds in low-pressure environments-as the solar neighborhood-is well matched by state-of-the-art turbulence-regulated models of star formation. However, these models substantially overpredict the low observed SFEs of clouds in high-pressure environments, which suggest the importance of additional physical parameters not yet considered by these models.