In this study, an incinerator is researched for the disposal of gaseous and liquid hazardous wastes (HWs) from the used lubricating oil refinery by incineration, following the zero-waste principle. Subsequently, combustion characterization of mixed-content HWs from different entrances of the combustion chamber in the incinerator, simultaneously with natural gas without mixing, is investigated experimentally, theoretically, and numerically. The HWs consist of gaseous ones from distillation and hydroprocessing and from the tank farm, and liquid ones resulting from petroleum refining processes. The results show that the combustion gases from HWs and natural gas are maintained at a minimum of 850 °C for at least 2 s in the 1.6 m diameter and 6 m length incinerator. The upper wall exhibits higher temperatures compared to the lower wall due to the heat generated during combustion, emphasizing the significance of material selection and design to withstand thermal stresses. A comprehensive analysis provides insights into the compatibility of the combustion chamber design with chemical processes, further underlining its contributions to environmental sustainability. Thus, this study demonstrates the effectiveness of mathematical and numerical analyses in improving the incineration process, ensuring the thorough combustion of hazardous waste, and minimizing the formation of harmful by-products.