This paper investigates the Raman-scattered O VI emission lines lambda lambda 6825, 7082 in symbiotic binaries using Monte Carlo simulations. The simulations calculate the scattering path of O VI lambda lambda 1032, 1038 line photons released from an extended emission nebula. A large fraction of these photons penetrate into the extended atmosphere and the wind of the cool giant, where Raman scattering, Rayleigh scattering and absorption take place. The employed formalism includes the polarization effects and the Doppler shifts introduced by the scattering processes. As a result, the simulations provide the flux, the integrated polarization and the spectropolarimetric structure of the Raman-scattered O VI lines. Additional results are the flux properties of the O VI lines in the far UV, and maps which visualize the scattering geometry. Results are presented in detail for four model geometries. They are supplemented by many additional computations in order to explore the model parameter space. The calculations are compared with the existing observational data of the Raman-scattered emission lines in symbiotic systems. The simulations are in general agreement with observations of the line strength, of the integrated polarization and of the phase-locked polarization variability. The simulations also reproduce the main features of the observed spectropolarimetric structure in the Raman-scattered lines. Further, the model results support the observed correlation of so-called type III profiles with systems having a red giant with strong mass-loss. The comparison between observations and simulations also reveals the limitations of the adopted scattering model. A major shortcoming of the present models is the two-dimensional (rotationally symmetric) geometry, which was introduced to limit the computational effort. Therefore the obtained results cannot account for the three-dimensional polarization structure observed in the Raman-scattered lines of many symbiotic systems. The computations neglect gas flows and radiative transfer effects in the nebular O VI emission tone. As a result, the computations give much less spectroscopically structured Raman lines than are observed. Nevertheless, it is found that symbiotic systems have preferentially an ionization geometry with an X-parameter X(H+) approximate to 2. Roughly speaking, this 'average' shape of the ionization front does not differ strongly from a plane between the two stellar components.