In recent years, techniques of intense THz laser have enabled us to experimentally observe nonlinear spin dynamics in antiferromagnets since the elementary excitations such as magnons reside on a THz to GHz range in antiferromagnets and THz laser thus can directly excite them. We numerically and theoretically investigate THz-laser or GHz-wave driven harmonic generations in typical ordered phases of antiferromagnets: N'eel, canted and weak ferromagnetic phases. The radiation waves (harmonic generations) are created by the incident-wave driven magnon dynamics. We point out that magnetic orders and phase transitions can change the spectra of harmonic generations, differently from those of metallic, semiconductor, or atomic-gas systems without (spontaneous) symmetry breakings. We consider both the magnon harmonic generation driven by standard single-color laser and that by two-color laser in the antiferromagnets, and find several dynamical symmetries and the corresponding selection rules of the harmonic generations. In particular, a special selection rule emerges in U(1)-spin-rotation symmetric magnetic phases (like ferromagnetic, ferrimagnetic, N'eel phases and U(1)-symmetric spin-liquid phases) irradiated by $C_{\ell }$-symmetric two-color laser. We also find that the computed spectrum in the weak ferromagnetic phase is consistent with a recent experiment of $\rm HoFeO_3$. These results indicate that the magnon harmonic generation spectra provide new information about symmetry or symmetry breaking of antiferromagnets.