A spinel oxynitride material in the form M3NO3 (M = B, Al, Ga, or In) is considered to be derived from a reaction of the form MN + M2O3 ---- M3NO3. Various possible phases of MN and M2O3 that could lead to M3NO3 oxynitride spinel material have been considered in the work. The structural, electronic, elastic properties and the relative stabilities of the bulk and the nature of the resulting vacancies or defect-related properties of these oxynitride spinel structures are investigated using ab-initio or first principles electronic structure methods based on density functional theory (DFT). Molecular dynamics simulations of bulk oxynitride spinel systems are also considered. Using a series of Tersoff empirical potentials, the different thermodynamic properties of these oxynitride structure for varying temperature are also predicted such as the Debye temperature, thermal expansion co-efficient and specific heat.