Abstract We use the EAGLE cosmological, hydrodynamical simulations to predict the column density and equivalent width distributions of intergalactic O vii ($E=574 \, \rm {eV}$) and O viii ($E=654 \, \rm {eV}$) absorbers at low redshift. These two ions are predicted to account for $40 \, \hbox{ per cent}$ 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 active galactic nucleus feedback, which strongly reduces the number of strong (column density $N \gtrsim 10^{16} \, \rm {cm}^{-2}$) absorbers. The distributions have a break at $N ∼ 10^{16}\, \rm {cm}^{-2}$, corresponding to overdensities of ∼102, likely caused by the transition from sheet/filament to halo gas. Absorption systems with $N \gtrsim 10^{16} \, \rm {cm}^{-2}$ 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 ${N}_{\rm {H}\, \rm {I}} \gtrsim 10^{15} \, \rm {cm}^{-2}$, 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.