We use the EAGLE cosmological, hydrodynamical simulations to predict the column density and equivalent width distributions of intergalactic O VII ($E=574$ eV) and O VIII ($E=654$ eV) absorbers at low redshift. These two ions are predicted to account for 40% of the gas-phase oxygen, which implies that they are key tracers of cosmic metals. We find that their column density distributions evolve little at observable column densities from redshift 1 to 0, and that they are sensitive to AGN feedback, which strongly reduces the number of strong (column density $N gtrsim 10^{16} , mathrm{cm}^{-2})$ absorbers. The distributions have a break at $N sim 10^{16} , mathrm{cm}^{-2}$, corresponding to overdensities of $sim 10^{2}$, likely caused by the transition from sheet/filament to halo gas. Absorption systems with $N gtrsim 10^{16} mathrm{cm}^{-2}$ are dominated by collisionally ionized O VII and O VIII, while the ionization state of oxygen at lower column densities is also influenced by photoionization. At these high column densities, O VII and O VIII arising in the same structures probe systematically different gas temperatures, meaning their line ratio does not translate into a simple estimate of temperature. While O VII and O VIII column densities and covering fractions correlate poorly with the H I column density at $N_{mathrm{H , I}} gtrsim 10^{15} , mathrm{cm}^{-2}$, O VII and O VIII column densities are higher in this regime than at the more common, lower H I column densities. The column densities of O VI and especially Ne VIII, which have strong absorption lines in the UV, are good predictors of the strengths of O VII and O VIII absorption and can hence aid in the detection of the X-ray lines.
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