The averaged stress and strain response functions of granular aggregates are investigated numerically. We use the discrete-element method (DEM) to generate granular packings consisting of soft convex polygonal particles, i.e., the simulation geometry is two-dimensional. Packings are prepared in a rectangular container. To determine the stress response of a packing, we apply an external load to a single grain from the top layer of the assembly, with a force small enough not to cause structural rearrangements. Measuring the average vertical normal stress response at different heights of the sample, we find that the shape of the stress response function depends on the regularity of the granular assembly. For packings with strong spatial order, the average stress response shows a behaviour corresponding to that of hyperbolic continuum equations. As the amount of contact disorder increases, there is no wavelike stress propagation anymore and a behaviour emerges that would rather be predicted by elliptic equations. Furthermore, we show that not only geometric disorder but also large values of static friction coefficients, which may be linked to force disorder, lead to elliptic equations. Finally, we determine the strain response for a rectangular sample that consists of monodisperse particles.