Various possible structures of ternary mononitrides of group 5 transition metals (V0.5Ta0.5N, V0.5Nb0.5N and Nb0.5Ta0.5N) are systematically explored in 0–300 GPa pressure range through CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method. Three possible phases with Pmm2, Cmc21, and Fm-3m space group have been uncovered. Their dynamical, mechanical and thermodynamic stabilities are checked through calculations of phonon spectra, elastic constants and formation enthalpy. The elastic anisotropies are fully investigated by the dependence of linear bulk, Young's and shear moduli on the crystal orientations. To study the strength of these three compounds, the compressive, tensile and indentation shear strengths are systematically studied from the first-principles calculations. The mononitrides with Pmm2 and Cmc21 structures exhibit much better mechanical property relative to VN, NbN and TaN with traditional B1 (NaCl-like) structure. Our results reveal that the Pmm2 and Cmc21 phases of these three compounds possess the strength values up to 30 GPa under the Vickers indentation simulation calculations, which are comparable to well-known WB3, WB4 and ReB2 reported as potential superhard transition metal borides. Additionally, the electronic structures of these mononitrides are also studied to explore the intrinsic chemical bonding nature, and a novel transition of semiconductor-to-conductor from V0.5Ta0.5N, V0.5Nb0.5N to Nb0.5Ta0.5N is exposed for the Fm-3m phases of these compounds.