We report on the energetics of molecular outflows in 14 local ultraluminous infrared galaxies (ULIRGs) that show unambiguous outflow signatures (P Cygni profiles or high-velocity absorption wings) in the far-infrared lines of OH measured with the Herschel/PACS spectrometer. All sample galaxies are gas-rich mergers at various stages of the merging process. Detection of both ground-state (at 119 and 79 μm) and one or more radiatively excited (at 65 and 84 μm) lines allows us to model the nuclear gas (≲300 pc) and the more extended components using spherically symmetric radiative transfer models. Reliable models and the corresponding energetics are found in 12 of the 14 sources. The highest molecular outflow velocities are found in buried sources, in which slower but massive expansion of the nuclear gas is also observed. With the exception of a few outliers, the outflows have momentum fluxes of (2-5) × L IR/c and mechanical luminosities of (0.1-0.3)% of L IR. The moderate momentum boosts in these sources (≲3) suggest that the outflows are mostly momentum driven by the combined effects of active galactic nuclei (AGNs) and nuclear starbursts, as a result of radiation pressure, winds, and supernova remnants. In some sources (˜20%), however, powerful (1010.5-11 L ⊙) AGN feedback and (partially) energy-conserving phases are required, with momentum boosts in the range of 3-20. These outflows appear to be stochastic, strong AGN feedback events that occur throughout the merging process. In a few sources, the outflow activity in the innermost regions has subsided in the past ˜1 Myr. While OH traces the molecular outflows at subkiloparsec scales, comparison of the masses traced by OH with those previously inferred from tracers of more extended outflowing gas suggests that most mass is loaded (with loading factors of \dot{M}/{SFR}=1{--}10) from the central galactic cores (a few × 100 pc), qualitatively consistent with an ongoing inside-out quenching of star formation. Outflow depletion timescales are <108 yr, shorter than the gas consumption timescales by factors of 1.1-15, and are anticorrelated with the AGN luminosity.