From the standpoint of thermal radiation, omnidirectional nonreciprocal thermal radiation (NTR) is strongly desired for thermal energy harvesting. Here, we propose theoretically lithographic free thermal emitter made in a dielectric-Weyl semimetal (WSM)-dielectric fashion and terminated by a metallic substrate. By engineering the structural parameters, a surprising result of spectrally selective as well as omnidirectional (along both polar and azimuthal angles) NTR is realized. It is shown that the magnitude and sign of the contrast between emission (e) and absorption (α) can be managed simultaneously. The suggested structure shows good nonreciprocity stability in a wide range of polar and azimuthal angles for transverse magnetic (TM) polarized incident wave. The ability to fine tune nonreciprocal radiative properties of our design suggests a relatively simple way to manifest the NTR with high performance, which could lead to the development of power scavenging and conversion devices.