Sensitivity to sub-pixel sample features has been demonstrated as a valuable capability of phase contrast x-ray imaging. Here, we report on a method to obtain angular-resolved small angle x-ray scattering distributions with edge-illumination- based imaging utilizing incoherent illumination from an x-ray tube. Our approach provides both the three established image modalities (absorption, differential phase and scatter strength), plus a number of additional contrasts related to unresolved sample features. The complementarity of these contrasts is experimentally validated by using different materials in powder form. As a significant application example we show that the extended complementary contrasts could allow the diagnosis of pulmonary emphysema in a murine model. In support of this, we demonstrate that the properties of the retrieved scattering distributions are consistent with the expectation of increased feature sizes related to pulmonary emphysema. Combined with the simplicity of implementation of edge-illumination, these findings suggest a high potential for exploiting extended sub-pixel contrasts in the diagnosis of lung diseases and beyond.