The ordered intermetallic γ-TiAl phase plays an important role in determining mechanical properties of engineering γ-TiAl based alloys. During alloy production, interstitial O is introduced in these alloys and in the γ-phase in particular. It is anticipated that it can have a significant impact on mechanical properties of the alloys due to localized dislocation pinning at O atoms and other point defects. In this paper, we apply a standard thermodynamic approach concerning point-defects in ordered compounds together with density functional theory and finite element method calculations to investigate the impact of O on thermal point defect formation and the associated defect formation eigenstrains in the practically relevant Ti-rich off-stoichiometric γ-TiAl phase. The results show that O is strongly bound to vacancies and Ti antisite defects and may substantially increase their equilibrium concentration. Calculated concentrations and eigenstrain values of antisites and vacancies in the presence of O offer a possibility of their interaction with dislocations, promoting dislocations pinning within the strain aging temperature regime of TiAl alloys.