In fact, a better list of useful herbal or aromatic oils would be Lavender, Wintergreen, Rosemary and Thuja.
Rosemary should be at the top of the list as an effective treatment for skin problems and muscle soreness. It is an ingredient of the commercial product Algyval at the level of about 10%. My impression is that the other ingredients are not active.
Lavender is a powerful antifungal. Both Lavender and Rosemary are not strong irritants and in many cases can be used directly on the skin without dilution.
A constituent of Wintergreen is methyl salicylate, related to acetyl salicylic acid, ASA, aka aspirin, the first commercial anti-inflammatory drug. Wintergreen oil should not be used internally and with caution on the skin. Salicylate the name is derived from salix the botanical name for willows; the original aspirin ingredient was isolated from willow bark. There are reports that excessive topical use of methyl salicylate in a commercial counter-irritant like Bengay has caused death, but also that the synthetic form is a mixture of isomers different from those in the natural oil.
Breathing Wintergreen oil can help headaches and respiratory congestion.
Many of the home made foot ointments used and sold by sled dog veterinarians were concocted using as a base a commercial pink ointment with artificial cedar or Thuja oil and zinc oxide. There are warnings about Thuja oil; one constituent, thujone is also present in Wormwood and blamed for the toxic effects of Absinthe, although some believe that the primary toxin in Absinthe was alcohol and that when it was banned and replaced by Pernod or Pastis or other alcoholic drinks, the working men and their families for whom this done suffered no less than before.
Thyme oil is a strong irritant and I don’t know any uses that are not better fulfilled with something else.