The quantum wave packet dynamics following a coherent electronic excitation of LiH by an ultrashort, polarized, strong one-cycle infrared optical pulse is computed on several electronic states using a grid method. The coupling to the strong field of the pump and the probe pulses is included in the Hamiltonian used to solve the time-dependent Schrodinger equation. The polarization of the pump pulse allows us to control the localization in time and in space of the nonequilibrium coherent electronic motion and the subsequent nuclear dynamics. We show that transient absorption, resulting from the interaction of the total molecular dipole with the electric fields of the pump and the probe, is a very versatile probe of the different time scales of the vibronic dynamics. It allows probing both the ultrashort, femtosecond time scale of the electronic coherences as well as the longer dozens of femtoseconds time scales of the nuclear motion on the excited electronic states. The ultrafast beatings of the electronic coherences in space and in time are shown to be modulated by the different periods of the nuclear motion.