The aim of the study was to analyze the effect of the type of gelling substance on the selected physicochemical properties of oleogels. Rapeseed oil (RO) and 5% w/w of one of the following structuring compounds (SC) were used for their production waxes: sunflower (SUN), candelilla (CAN), bees white (BW), bees yellow (BY), or monoacylglycerols (MAG). The ability of SC to form a network in RO was assessed on the basis of an analysis of the texture of oleogels (hardness and spreadability test, stability determined by the centrifugal method). Oxidative stability was determined using the Rancimat test. In addition, the microstructure of an oleogel samples was observed at a magnification of 600 times in polarized light and in a bright field. Differences in the brightness and color of the samples were also assessed using the CIELab reflection method. The highest hardness (5.52 N) and physical stability (99.67%) were found in oleogel with candelilla wax. A higher value of the force causing deformation of the sample indicates a denser network of oil gel, which was confirmed by the microscopic images analyzed in the work. The organogel with CAN had the shortest (on average 8.49 nm) and the most regularly distributed crystals compared to other samples. The lowest values of organogel strength and spreadability test parameters (e.g., firmness, work of shear, stickness, work of adhesion), which were respectively 0.73 N, 4.39 N, and 9.74 N mm, while −4.87 N and −2.68 N mm were obtained with the variant, which was yellow beeswax. Considering the texture results obtained and the centrifugal stability, it was found that organogels with yellow beeswax were characterized by the worst structuring of rapeseed oil. Sunflower wax was considered the best among the analyzed gelling agents (under the conditions of the experiment). The organogel with its 5% w/w share was distinguished by the closest to the white color and texture most reminiscent of cream. In addition, it had the highest work of shear value and the longest induction time (6.8 h) in the Rancimat test.