© 2017 American Physical Society. The structural properties, energetics, and polarizations of perovskite-based thin-film oxide systems are computed as a function of biaxial strain state and epitaxial orientation, employing an automated computational workflow based on density functional theory. A total of 14 compositions are considered, of the form ABO3, with A = Ba, K, Na, Pb, and Sr and B = Hf, Sn, Ti, Zr, Nb, Ta, and V site cations chosen to yield tolerance factors with values ranging between 0.95 and 1.1. Three biaxial strain states corresponding to epitaxial growth of (100)-, (110)-, and (111)-oriented films are considered, with misfit strains ranging between -4% to 4%. Results are presented for the series of perovskite-derived phases, and their corresponding symmetries, which are energetically favorable as a function of misfit strain, along with their corresponding equilibrium atomic positions, lattice parameters, and electric polarizations. The results demonstrate robust trends of in-plane polarization enhancement under tensile strain for all epitaxial orientations, and out-of-plane polarization enhancement with compression for the (100)- and (110)-oriented films. Strains corresponding to the (111)-growth orientation lead to a wider variety of out-of-plane polarization behavior, with BaTiO3 showing anomalous diminishing polarization with compression. Epitaxial orientation is shown to have a strong effect on the nature of strain-induced phase transitions, with (100)-oriented systems tending to have smooth, second-order transitions and (110)- and (111)-oriented systems more commonly exhibiting first-order transitions. The significance of this effect for device applications is discussed, and a number of systems are identified as potentially interesting for ferroelectric thin-film applications based on energetic stability and polarization behavior. Analysis of polarization behavior across different orientations reveals distinct groups into which compositions can be organized, some of which have polarization dependencies on misfit strain that have not been reported previously.