For instance, in Russian there is an adjective "oily", which means a liquid of high viscosity. Is this assertion even true in general or statistically?
Viscosity depends on the intermolecular forces between molecules. Typically, the more viscous a substance or liquid is, the stronger its intermolecular forces are. In polar solvents, there are dipole-dipole interactions while in non-polar solvents, there are London Dispersion Forces. Sometimes, when individual molecules are large, LDF can be stronger than dipole-dipole interactions in some polar solvents. The point is that having stronger intermolecular forces will lead to higher viscosity, and being polar doesn't mean it will have stronger IMF than non-polar substances.