Oat-based products are characterized by high fat content with a favorable fatty acid composition. It is of great importance to control the quality of fat fraction as an important indicator of food product safety. The aim of this study was to analyze fat isolated from whole grain oatmeal, mountain oatmeal, and instant oatmeal. We determined the composition of fatty acids and the distribution of fatty acids in triacylglycerol positions using gas chromatography. The oxidative stability of the tested fat was evaluated using pressure differential scanning calorimetry. Melting profiles were determined by differential scanning calorimetry. It was found that fat isolated from oat products is a rich source of unsaturated fatty acids. In the sn-2 position of triacylglycerols, the highest share of oleic acid was found. The fat was characterized by the highest proportion of linoleic acid in the sn-1,3 positions of the triacylglycerols. It was observed that the induction time of oxidation process of fat reached the values of 28.79 min–39.07 min in a test conducted at 120 °C and 5.84 min–7.37 min at 140 °C. The analyzed melting profiles showed the presence of peaks indicating the presence of low-melting triacylglycerols containing mainly unsaturated fatty acids.