I have worked in the "used oil" recovery industry for over 15 years making #5 "spec" fuel for asphalt plant burners (before most went to LNG) and there are two main themes to follow to make fuel from used (not waste, never use the term "waste" for a recovered product) oils.
Mainly getting the solids out but the water content too, under 5% H2o will work pretty well, much more and it may run okay but it kills the BTU's (and power!!). The second is as mentioned above synthetics, semi synthetics are as you may deduce partially petroleum, the full type is of course not. Mostly the consideration with 100% synthetics is being able to get the molecule chains to bond (mix without separation) to the petroleum chains. One of the easiest ways to do this is to add about 1% acetone to the blend, acetone will bond with both molecule chains and prevent separation.
A word of caution about used hydraulic oil, make sure it is not fire resistant, this type is found mainly in aircraft or rescue settings as well as some chemical operations using hydraulic powered blending equipment because the product being produced has too many unstable (volatile) ingredients to use electric powered blending equipment.
Yes I do used recovered oils (blended with about 40-50% virgin diesel) to to power my mechanical fueled diesels (453 Detroit powered loader, Case 580D and my 1993 Ford "Super Duty), it only makes sense!