The present invention addresses the processing of waste and low-value products to produce useful materials in reliable purities and compositions, at acceptable cost, and with high energy efficiency. In particular, the invention comprises a multi-stage process that converts various feedstocks such as offal, animal manures, municipal sewage sludge, that otherwise have little commercial value, to useful materials including gas, oil, specialty chemicals, and carbon solids. The process subjects the feedstock to heat and pressure in a reducing environment accomplished by controlled addition of sulfur and sodium, separates out various components, then further applies heat and pressure to one or more of those components. The invention further comprises an apparatus for performing a multi-stage process of converting waste products into useful materials, and at least one oil product that arises from the process.