Based on first-principles methods and Boltzmann transport theory, we investigated the biaxial strain effects on electronic and thermoelectric properties of three group-III nitrides (BN, AlN and GaN) 2D honeycomb mono-layered nanosheets. The direct-indirect band gap transitions occurred for BN and GaN nanosheets when the strain was applied. In addition, the band gaps decreased with increase of tensile strain; and we uncovered the mechanism behind by the total and projected density-of-state (PDOS) analyses. At the same time, we presented the contour plots of their electrical transport properties as a function of both temperature and carrier concentration at strain-free states. Power-factors of BN, AlN and GaN nanosheets were also calculated. We found only peak power factors of p-type GaN and n-type BN showed a strong dependence on biaxial strain. Such differences of the strain-dependent thermoelectric performance among BN, AlN and GaN may be due to the competition between covalency and ionicity in these 2D structures. Our results provide a new avenue to optimize thermoelectric properties of 2D nanosheets by strain engineering.