The present invention relates to the conversion of waste and low-value materials into useful products in reliable purities in a cost-effective and energy-efficient manner. More specifially, the invention provides processes that can handle mixed streams of various feedstocks, e.g. shredder residue, offal, animal manures, municipal sewage sludge, tires, and plastics, that otherwise have little commercial value, to useful products including gas, oil, specialty chemicals, and carbon solids. The process subjects the feedstock to heat and pressure, separates out various components, then further applies heat and pressure to one or more of those components, according to processes based on thermal or catalytic cracking. The invention further comprises an apparatus for performing a multi-stage process of converting waste materials into useful materials, and at least one oil product that arises from the process. Useful products can also be obtained or derived from materials diverted at different points of the process.