Inorganics are pesticides without carbon which can be natural earth minerals or man-made compounds. Acts mainly as a desiccant and is rarely useful in landscapes unless combined with an insecticide like pyrethrin. Sulfur - an ancient control for insects and mites. Since it is a stomach poison, it does not adversely affect beneficial predators and parasites. Good only against leaf feeding caterpillars, sawflies and beetles.
Oils are petroleum or plant based hydrocarbon chains which have insecticidal activity.
When used in winter, has minimal adverse affect on beneficial insects. Usually combined with other insecticides such as soaps. Fatty Acid Salts or Soaps are man made hydrocarbons using an ion, usually potassium or sodium, to join together fatty acid chains. Fatty acid chains containing 6 to 10 carbons have insecticidal properties. Insecticidal soaps apparently disrupt cell membranes.