Recent research focuses on new biodiesel production and purification technologies that seek a carbon-neutral footprint, as well as cheap, renewable and abundant raw materials that do not compete with the demand for food. Then, many attractive alternatives arise due to their availability or low-cost, such as used cooking oil, Jatropha oil (non-edible) or byproducts of vegetable oil refineries. Due to their composition and the presence of moisture, these oils may need a pretreatment to reach the established conditions to be used in the biodiesel production process so that the final product complies with the international quality standards. In this work, a solid catalyst based on 10 wt % sodium oxide supported on mesoporous silica SBA-15, was employed in the transesterification of different feedstocks (commercial sunflower and soybean oil, used cooking oil, acid oil from soapstock and Jatropha hieronymi oil) with absolute methanol in the following reaction conditions—2–8 wt % catalyst, 14:1 methanol to oil molar ratio, 60 °C, vigorous magnetic stirring and 5 h of reaction. In this way, first- and second-generation biodiesel was obtained through heterogeneous catalysis with methyl ester yields between 52 and 97 wt %, depending on the free fatty acid content and the moisture content of the oils.