The effect of steady-shear flow on the microstructure of nonaqueous dispersions of colloidal silica spheres having medium-range repulsive potentials is studied, with a newly developed two-dimensional light-scattering set-up, as a function of shear rate gamma and particle volume fraction phi. When dispersed in a close refractive index matching solvent mixture of ethanol and toluene, the dispersions exhibit an equilibrium disorder-order transition at phi = 12.6%. It is found that the shear deformation of the colloidal liquid structure at high shear rates is a smooth process with no long-range string or layer ordering in the flow-vorticity plane. The structure distortion is in good qualitative agreement with an approximate solution of the two-particle Smoluchowski equation. In particular, the theoretically recognized boundary-layer effect, which has been implicitly known for its relation to the onset of the non-Newtonian behaviour of effective viscosity, is clearly shown in our experiment for the first time. In the crystal phase an applied shear flow leads to the gradual melting of the equilibrium solid-like structure into sliding layers, strings, and finally into a distorted liquid-like structure as gamma is raised. There is also an indication that the layer structure contains a significant number of free strings. No shear-thickening or discontinuous behaviour in dispersion viscosity in relation to these translational order transitions is detected. We conclude that the nonequilibrium order of our system is correlated to the corresponding microstructure in equilibrium.