Excitation of Dyakonov surface waves guided by a plane wave incident on a columnar thin film (CTF) deposited on a surface-relief grating decorating a dielectric substrate was studied using the rigorous coupled-wave approach, when the grating plane, the plane of incidence, and the morphologically significant plane of the CTF are all different. The absorptance for a specific linear polarization state of the incident plane wave was plotted as a function of the polar angle of incidence, at a fixed azimuthal angle, and those absorptance peaks were identified that are independent of the thicknesses of the CTF and the dielectric substrate. The angular locations of these absorptance peaks were correlated with the solution of the canonical boundary-value problem for surface-wave propagation. Dyakonov surface waves can be excited in a wider range of directions in the interface plane by p-polarized illumination than by s-polarized illumination. When the incidence and the grating planes do not coincide, it is possible to excite Dyakonov surfaces for multiple values of the polar angle of incidence.