This work reexamines the insertion of O atoms in the L10 γ-TiAl system using first-principles calculations and thermodynamic modeling in the independent point defect approximation. It includes a study of intrinsic point defects, the insertion of many alloying elements (more than twenty were considered), as well as a study of their interaction with oxygen. The formation of complex defects composed of either vacancies, anti-sites or solute elements is then studied. Results at the atomic scale show a high segregation of oxygen in titanium-rich environments: oxygen easily segregates onto Ti anti-sites (Ti Al) and alloying elements are located in the vicinity of Al sub-lattices. DFT point-defect energetics shows that there is a clear correlation between the nature and site preference of an alloying element, and the oxygen segregation energy in the vicinity of this solute. The thermodynamic model shows that at equilibrium, oxygen does not occupy isolated interstitial sites but prefers to be located in the vicinity of Ti anti-sites or alloying elements. The effect of this strong segregation on oxygen diffusivity is discussed hereinafter. Results show a strong slowdown in oxygen diffusivity due to intrinsic defects. For Ti/Al > 0.5 ratios, the traps for O diffusion are mainly constituted by Ti anti-sites, and the addition of solutes does not contribute much to the trapping of diffusing O atoms. For Ti/Al < 0.5 ratios however, the contribution of solutes to trapping phenomena can be very important, and a decrease by 1-2 orders of magnitude of effective O diffusion coefficients can be observed for temperatures around 800-1100 K.