The nonlinear Navier-Stokes-Langevin equations are used to describe fluctuations in a compressible fluid with uniform shear flow. The hydrodynamic modes for small deviations from the macroscopic nonequilibrium state are calculated, including linear mode coupling of the fluctuating variables with the macroscopic velocity field. The associated correlation functions are determined with the full nonlinear dependence on shear rate required for long times and/or large shear rate. The stationary and joint probability densities are also constructed from the associated Fokker-Planck equation. As an application of these results, the lowest-order mode-coupling contributions to the renormalized shear viscosity are evaluated.