The very neutron-rich oxygen isotopes O-25 and O-26 are investigated experimentally and theoretically. The unbound states are populated in an experiment performed at the R3B-LAND setup at GSI via proton-knockout reactions from F-26 and F-27 at relativistic energies around 442 and 414 MeV/nucleon, respectively. From the kinematically complete measurement of the decay into O-24 plus one or two neutrons, the O-25 ground-state energy and width are determined, and upper limits for the O-26 ground-state energy and lifetime are extracted. In addition, the results provide indications for an excited state in O-26 at around 4 MeV. The experimental 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.