1H Nuclear Magnetic Resonance relaxometry studies have been performed for fifteen kinds of oil. The measurements of 1H spin-lattice relaxation rates have been carried out in a frequency range encompassing three orders of magnitude: from about 10 kHz to 10 MHz, at room temperature. The data have been analysed in terms of a rigorous model rendering translation diffusion coefficients and providing some insight into rotational dynamics of triacylglycerols molecules. It has been observed that the diffusion is approximately by about 200 times slower compared to water diffusion in bulk and the diffusion coefficient varies in a narrow range. The diffusion coefficients have been combined with viscosity for different kinds of oil. A relationship between the molecular (the diffusion coefficient) and macroscopic (the viscosity coefficient) quantities have been established. It has turned out that most of oils follows the revealed relation. Discrepancies from the relationship, observed for some oils, have been discussed.