We investigate a GaAs/(Ga,Al)As Fabry-Perot microcavity, into which (In,Ga)As quantum wells have been inserted. The cavity is wedge shaped, i.e., the detuning between the bare-exciton resonance and the bare optical cavity mode depends on the spatial position on the sample. Linear transmission spectra reveal a well-resolved Rabi splitting of 8 meV at resonance, an inhomogeneously broadened exciton transition of 4-5-meV width, and an 0.7-meV-wide Fabry-Perot mode. The time-resolved transmission exhibits deep beatings and a subpicosecond exponential decay: a behavior similar to that foreseen in the strong-coupling regime and in the absence of electronic disorder. Conversely, the four-wave mixing response appears weakly influenced by the cavity and not much different from what is expected for bare excitons. A photon echo, dephasing times as long as 50 ps, and only weak Rabi oscillations are observed. The experimentally observed features can be explained by a model based on the numerical solutions of the Maxwell-Bloch equations. This model confirms the dramatic influence structural disorder in the quantum wells has on the coherent nonlinear exciton-photon dynamics.