Recently, ferroelectric behavior was observed in compressed SrTaO2N thin films epitaxially grown on SrTiO3 substrates. Piezoresponse force microscopy measurements revealed small domains (101–102 nm) that exhibited classical ferroelectricity, a behavior not previously observed in perovskite oxynitrides. The surrounding matrix region exhibited relaxor ferroelectric-like behavior. Bulk SrTaO2N samples do not show ferroelectricity, thus suggesting that the origin of it may be related with the strain induced by the substrate. Ab-initio calculations reported that the small domains and the surrounding matrix had trans-type and a cis-type anion arrangements, respectively, but do not describe the experimentally observed equilibrium phase, nor the strain dependent polarization. In this work, we present high accurate all-electron first-principles calculations on the different possible local structures that can explain the ferroelectric-like properties of the strained material. The determined local structure and oxygen/nitrogen ordering has been related with polarization and epitaxial strain. The potential energies and polarization as functions of the in-plane lattice constant are reported.