We study theoretically the generation of coherent, anharmonic phonon-polariton responses through impulsive stimulated Raman scattering with intense, crossed ultrafast excitation pulses. We find that the refractive index appears modulated at the stimulated scattering wave vector and the corresponding phonon-polariton frequency, and, due to anharmonicity, at stimulated scattering wave vector overtones and their corresponding frequencies. A realistic model of the soft lattice vibrational mode of the ferroelectric crystal lithium tantalate is considered in detail. Specific predictions for the magnitudes of different wave vector overtone contributions to the lattice displacement are made compared to experimental observations of anharmonic lattice responses.