© 2016 American Physical Society. Thermal neutron capture γ-ray spectra for O16,17,18 and H2 have been measured with guided cold neutron beams from the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM II) reactor and the Budapest Research Reactor (BRR) on natural and O17,18 enriched D2O targets. Complete neutron capture γ-ray decay schemes for the O16,17,18(n,γ) reactions were measured. Absolute transition probabilities were determined for each reaction by a least-squares fit of the γ-ray intensities to the decay schemes after accounting for the contribution from internal conversion. The transition probability for the 870.76-keV γ ray from O16(n,γ) was measured as Pγ(871)=96.6 ±0.5% and the thermal neutron cross section for this γ ray was determined as 0.164±0.003 mb by internal standardization with multiple targets containing oxygen and stoichiometric quantities of hydrogen, nitrogen, and carbon whose γ-ray cross sections were previously standardized. The γ-ray cross sections for the O17,18(n,γ) and H2(n,γ) reactions were then determined relative to the 870.76-keV γ-ray cross section after accounting for the isotopic abundances in the targets. We determined the following total radiative thermal neutron cross sections for each isotope from the γ-ray cross sections and transition probabilities; σ0(O16)=0.170±0.003 mb; σ0(O17)=0.67±0.07 mb; σ0(O18)=0.141±0.006 mb; and σ0(H2)=0.489±0.006 mb.