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Oxidation strongly influences the properties of magnetic layers employed in spintronic devices. We study the effect of oxidation on the structural, magnetic, and electrical properties as well as current-induced spin-orbit torques (SOTs) in Pt/Co/AlOx, Pt/CoOx/Co/AlOx, and PtOx/Co/AlOx layers. We show how the saturation magnetization, perpendicular magnetic anisotropy, anomalous Hall resistance, and SOT are systematically affected by the degree of oxidation of both the Pt/Co and Co/Al interfaces. Oxidation of the Co/Al interface results in a 21% and 42% variation of the dampinglike and fieldlike SOT efficiencies, which peak at 0.14 and 0.07, respectively. The insertion of a paramagnetic CoOx layer between Pt and Co maintains a very strong perpendicular magnetic anisotropy and improves the dampinglike and fieldlike SOT efficiencies, up to 0.26 and 0.20, respectively. In contrast with recent reports, we do not find that the oxidation of Pt leads to a significant enhancement of the torques. Rather, we find that oxygen migrates from Pt to the Co and Al layers, leading to a time-dependent oxidation profile and an effective spin Hall conductivity that decreases with increasing oxygen concentration. Finally, we study current-induced switching in Pt/Co/AlOx with different degrees of oxidation and find a linear relationship between the critical switching current and the effective magnetic anisotropy controlled by the oxidation of Al. These results highlight the importance of interfaces and oxidation effects on the SOT and magnetotransport properties of heavy metal/ferromagnet/oxide trilayers and provide information on how to improve the SOT efficiency and magnetization-switching characteristics of these systems.