Reliable and precise knowledge about the strain and composition effects on the bandgaps and band offsets for the III-nitrides based heterostructures is crucial for the optimization of device structures. We present a nonorthogonal tight binding theory (H. Ünlü, Phys. Stat. Sol. (b), 235, pp 248-253, 2003 ) to investigate the interface misfit, thermal expansion gradient and pressure induced strain and composition effects on band offsets in pseudomorphic InGaN/GaN, AlGaN/GaN, GaAsN/GaAs, and AlGaAsN/GaAs heterostructures with zinc-blende structures. The model considers the nonorthogonality of hybrids of adjacent atoms and the interaction of bonding and antibonding states at high symmetry points (e.g., , L and X) in calculating the valence band energies of semiconductors. The valence band offsets are then obtained from the difference between the valence band energies, screened by the optical dielectric constants of constituent semiconductors. Model predictions compare well with experiment (H. Morkoç et al.,Semiconductors and Semimetals, 50, 193, Academic, 1998) for the band offsets of nitride systems. Simulations show that the valence band offset in AlGaN/GaN system is small but in the InGaN/GaN system is very large. Tensile strain in AlGaN leads to positive bowing of the conduction band offsets in AlGaN/GaN system and the compressive strain in InGaN leads to negative bowing of conduction band offsets in InGaN/GaN system as a function of composition.