We present a nonequilibrium many-body formulation of the coherent ultrafast nonlinear optical response of doped semiconductors and systems with a strongly correlated ground state, such as the quantum Hall system (QHS). Our theory is based on a truncation of the density-matrix equations of motion in the absence of a small interaction parameter, obtained by expanding in terms of the optical field and by using Hubbard operator density matrices to describe the exact dynamics within a subspace of many-body states. We identify signatures of noninstantaneous interactions between magnetoexcitons (X) and the incompressible two-dimensional electron gas (2DEG) during femtosecond and picosecond time scales by describing X coupling to inter-Landau-level magnetoroton (MR) and magnetoplasmon excitations. We show that strong X coupling to X+MR configurations changes the temporal evolution of the nonlinear optical spectra as compared to the random-phase approximation (RPA). We calculate the three-pulse four-wave mixing signal, whose dependence on frequency and two time delays reflects the dephasing and relaxation of the strongly coupled X-2DEG system, and demonstrate that the dynamics of the X-2DEG interaction process can be resolved with femtosecond optical pulses. Our results shed light into unexplored subpicosecond and coherent dynamics of the QHS and may be used to interpret and guide two-dimensional correlation spectroscopy experiments. © 2010 The American Physical Society.