We report experimental three-phase oil relative permeability in two water-wet media (a sandpack and a Berea sandstone core) along different saturation paths. Three oils with different viscosities, compositions, and spreading coefficients were used in the measurements. The data show that oil relative permeability can vary significantly along different saturation paths. Most importantly, we find that despite the significant (orders of magnitude) variation of oil relative permeability along different saturation paths, the oil relative permeability in each medium can be collapsed into a single relative permeability curve, once they are plotted as a function of mobile oil saturation. However, this collapsed curve varies depending on the porous media. We show that the same behavior occurs in the relative permeability data published over the past 50 years. These observations indicate that the key factor in differences between oil permeabilities in the same porous media is changes in the residual oil saturation. We examine the performance of most commonly used relative permeability models, i.e., Corey, Saturation-Weighted Interpolation (SWI), and Stone against our data. Given the importance of residual oil saturation, we fit the experimental data along different saturation paths by treating the residual oil saturation in these models as the fitting parameter while keeping the other parameters constant. We find that the Corey and SWI models fit the data very well while the Stone model performs poorly at low saturations. We find that residual oil saturation is a nonlinear function of gas/water saturation as opposed to linear relationship previously suggested by others.