The structural responses of a polymer-clay nanocomposite hydrogel to an imposed shear field are investigated from the nanometer to the micrometer length scales. The effects of polymer molecular weight and concentration of the components are probed, and the structural response of the individual components is explored using contrast matching techniques with small-angle neutron scattering. At rest the clay structure appears minimally perturbed by the presence of the polymer. As the network begins to be disrupted under the effect of low shear, large-scale inhomogeneities roll up and orient with their long axis parallel to the neutral direction. With increasing shear rates the effect of the polymer-clay interactions becomes apparent with nanoscopic orientation of both the clay platelets and the polymer chains, but only in systems where polymer bridging of the clay can occur. The clay and polymer concentration dependence of the shear response suggests an ideal combination of concentrations and polymer molecular weights with implications for materials design.