The very neutron-rich oxygen isotopes 25O and 26O are investigated experimentally and theoret- ically. In this first R3B-LAND experiment, the unbound states are populated at GSI via proton- knockout reactions from 26F and 27F at relativistic energies around 450 MeV/nucleon. From the kinematically complete measurement of the decay into 24O plus one or two neutrons, the 25O ground- state energy and lifetime are determined, and upper limits for the 26O ground state are extracted. In addition, the results provide evidence for an excited state in 26O at around 4 MeV. The ex- perimental findings are compared to theoretical shell-model calculations based on chiral two- and three-nucleon (3N) forces, including for the first time residual 3N forces, which are shown to be amplified as valence neutrons are added.