This study investigates the temperature- and pressure-dependent thermodynamic and mechanical properties of zirconium oxides and suboxides, which is critical for understanding the oxidation/corrosion behaviors of Zr alloys in extreme conditions. Using the first-principles approach, we systematically evaluated the structural, thermodynamic, and mechanical properties of m-ZrO2, t-ZrO2, ZrO, Zr2O, Zr3O, and Zr6O at a wide range of temperatures from 0 to 1600 K and pressures from 0 to 12 GPa. The calculated lattice parameters agree well with the experimental measurements. Moreover, the formation enthalpy and phonon dispersion results indicate that these Zr-O compounds are both thermodynamically and dynamically stable. In particular, ZrO exhibits the largest elastic modulus and hardness among the six Zr-O compounds. The mechanical behaviors vary with temperature and pressure, where m-ZrO2, t-ZrO2, Zr3O, and Zr6O exhibit ductile characteristics, while ZrO and Zr2O undergo a brittle-ductile transition with the change of temperatures and pressures. This work enhances our understanding of the stability of Zr-O phases at different temperatures and pressures, and also provides insights into larger-scale modeling of the microstructural evolution and mechanical properties of Zr alloys during high-temperature oxidation.