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Competing interactions in quantum materials can tip over the ground state on the verge of phase transitions. We report such effects in the strongly correlated metal, Ca₃Ru₂O₇, where symmetry-breaking optical phonons are shown to modulate the pseudogap as well as mediate density wave like fluctuations.  Combining temperature dependent Raman spectroscopy with density functional theory, we crucially rectify prior symmetry assignments for phonons.  This reveals two dominant and competing B₂ phonons that exhibit a cross-over change of Raman scattering across the metal-pseudogap transition. This is shown to be a consequence of a strong electron-phonon coupling of ~10 eV/Å  (comparable with graphene), as one of these phonons modulates the ground state structure closer to the pseudogap phase, while the other away from it and towards the metallic phase. A microscopic model reveals that this arises from the phonons modulating the Ru 4d orbital splitting and the bandwidth of the in-plane electron hopping. Moreover, the B₂ phonons mediate incoherent dynamical charge and spin density wave fluctuations, which are evidenced by a symmetry-dependent change in the background electronic Raman scattering. This study broadly reveals the crucial role of phonons with strong electron-phonon coupling (polarons) in enabling the electronic and magnetic phase transitions in quantum materials.