Recently, a fast and accurate approximate QP method, based on the DFT-1 /2 method, the DFT+A-1 /2 scheme, has been developed for calculating band structures of compounds with cations featuring shallow core levels. This method not only provides fundamental gaps in excellent agreement with GW calculations and experimental measurements but also determines d-band positions. The method has been demonstrated for wurtzite, rocksalt and zincblende ZnO and CdO. Given the predictive power of the DFT+A-1 /2 scheme, we will apply it to much more complex oxides with crystallographic structures that contain many atoms in the unit cell. This paper briefly describes the methodology for deriving atomic structures, computing their energetics, calculating approximate QP band structures, and predicting exciton binding energies. We then investigate the atomic geometries, use the resulting atomic positions to calculate complete band structures -including gaps, effective masses, transition energies, and positions of Ga 3d and In 4d levels -and include an examination of optical and dielectric properties. The resulting dielectric constant tensors and effective masses are used to estimate the binding energies of band-edge excitons for all polymorphs. Finally, we present a summary and conclusions.