Neutron resonance analyses have been performed for the capture cross sections of 186Os, 187Os, and 188Os measured at the n_TOF facility at cern. Resonance parameters have been extracted up to 5, 3, and 8 keV, respectively, using the sammy code for a full R-matrix fit of the capture yields. From these results average resonance parameters were derived by a statistical analysis to provide a comprehensive experimental basis for modeling of the stellar neutron capture rates of these isotopes in terms of the Hauser-Feshbach statistical model. Consistent calculations for the capture and inelastic reaction channels are crucial for the evaluation of stellar enhancement factors to correct the Maxwellian averaged cross sections obtained from experimental data for the effect of thermally populated excited states. These factors have been calculated for the full temperature range of current scenarios of s-process nucleosynthesis using the combined information of the experimental data in the region of resolved resonances and in the continuum. The consequences of this analysis for the s-process component of the 187Os abundance and the related impact on the evaluation of the time duration of galactic nucleosynthesis via the Re/Os cosmochronometer are discussed.