The in-plane oxygen vibrations in La₂NiO₄ are investigated for several hole-doping concentrations both theoretically and experimentally via inelastic neutron scattering. Using an inhomogeneous Hartree-Fock plus random-phase approximation numerical method in a two-dimensional Peierls-Hubbard model, it is found that the doping induces stripe ordering of localized charges, and that the strong electron-lattice coupling causes the in-plane oxygen modes to split into two subbands. This result agrees with the phonon band splitting observed by inelastic neutron scattering in La_2-xSr_xNiO₄. Predictions of strong electron-lattice coupling in La₂NiO₄, the proximity of both oxygen-centred and nickel-centred charge ordering, and the relation between charged stripe ordering and the splitting of the in-plane phonon band upon doping are emphasized.