Recent advances indicate that enhanced light-matter interaction in plasmonic nanocavities can create hybrid properties in integrated plasmonic metal nanostructures and soft materials. Here, by integrating polyelectrolytes and surface ligands in gold nanorod-on-mirror nanocavities and detecting the nanocavity resonance and vibrational Raman scattering simultaneously, we found that the plasmon-vibration interaction modifies both the nanocavity and molecular responses. Large enhancement of Raman scattering accompanied by the plasmon resonance linewidth broadening are observed as the laser-plasmon detuning approaches the CH vibrational frequency of the molecular systems in the nanocavities. The experimental observations are consistent with the molecular optomechanics theory that predicts dynamical backaction amplification of the vibrational modes and high sensitivity of Raman scattering when the plasmon resonance overlaps with the Raman emission frequency. The results presented here suggest that molecular optomechanics coupling may be manipulated for creating hybrid properties based on quantum mechanical interaction of molecular oscillators and nanocavity electromagnetic optical modes.