In this paper, we have performed thorough analyses of volumetric and viscosity data for six oils. The volumetric data has been inspected by using two different equations of state, drawing a special attention to the intersection of the isothermal pressure dependences of the thermal volume expansivity, which were earlier reported for various materials in the liquid state. Each fluid is unique with respect to the other oils’ relative composition, with those being either a pure liquid (Sebacate), or mineral oil with a proprietary blend of branched paraffins, napthalenes and aromatic molecules (Normafluid) or are undisclosed composition of mineral oil (MIN-H01 and MIN-H02) or are composed of fatty acid methyl esters (soybean biodiesel and rapeseed biodiesel). We have confirmed that the intersection points evaluated for different isotherms constitute a nonlinear curve for a given tested oil, and not any single point or straight line. Consequently, we have determined the temperature–pressure areas important from the application viewpoint, within which the thermal volume expansivity behaves differently, either increasing or decreasing with increasing temperature at a constant pressure. In the viscosity analysis, the parametrizations of the temperature–pressure dependences of specific volume based on the equations of state enabled to employ the density scaling idea in its simplest form of a power law of densityγ/temperature, where γ related to an effective intermolecular potential is independent of thermodynamic conditions to a good approximation, which was successfully validated by various materials mainly in the supercooled liquid state, but also in the normal liquid and liquid crystal states in some cases. We have found that the scaling law giving prediction benefits relied on a linkage between macroscopic measurement quantities and effective molecular interactions is obeyed by the viscosity data of examined oils. Then, based on the prediction capabilities of the density scaling criterion, we have successfully explored the inflection points observed in some isothermal pressure dependences of viscosity measured for the oils in the temperature–pressure ranges that differ from those earlier reported for other materials. This intriguing finding observed in case of the experimental data for only some examined oils yields not only cognitive benefits, but it is also expected to exert an effect for instance on mechanical properties of the materials. Thus, our comparative discussion about the intersection and inflection curves provide a useful contribution to the further investigations of these thermodynamic and dynamic issues and other physicochemical properties of oils, which require gaining a better insight.