Incinerators to burn the kind of refuse you mention are sometimes built with two sections: a 30-35o inclined section for drying, and a horizontal burn-out section provided with an auxiliary burner. An after-burning pot and an ash catch pot sometimes must be added.
A complete welded elliptical cylinder made in two parts as above, complete with concrete refractory, grid, ash doors, air doors, and one burner can be purchased with a grid capacity of 150-200 kg/h/m2 of dry refuse.
For earth contaminated with oil, some kind of rotating kiln appears to be the most suitable. Feed can be done from a simple hill-like device or by the help of a feeding machine.