The ratios of the three stable oxygen isotopes 16O, 17O, and 18O on the Earth and, as far as we know in the Solar system, show variations on the order of a few per cent at most, with a few outliers in meteorites. However, in the interstellar medium there are some highly fractionated oxygen isotopic ratios in some specific molecules. The goal of this work is to investigate the oxygen isotopic ratios in different volatile molecules found in the coma of comet 67P/Churyumov–Gerasimenko and compare them with findings from interstellar clouds in order to assess commonalities and differences. To accomplish this goal, we analysed data from the ROSINA instrument on Rosetta during its mission around the comet. 16O/18O ratios could be determined for O2, methanol, formaldehyde, carbonyl sulfide, and sulfur monoxide/dioxide. For O2 the 16O/17O ratio is also available. Some ratios are strongly enriched in the heavy isotopes, especially for sulfur-bearing molecules and formaldehyde, whereas for methanol the ratios are compatible with the ones in the Solar system. O2 falls in-between, but its oxygen isotopic ratios clearly differ from water, which likely rules out an origin of O2 from water, be it by radiolysis, dismutation during sublimation, or the Eley–Rideal process from water ions hitting the nucleus as postulated in the literature.