Hello, I'm so sorry to hear about your fellow Watson and I'd like to help.
Fragrant oils can be very irritating to both the skin and the mucous membranes in his mouth, esophagus and stomach.
If this just happened or if you can still see evidence of the oil then washing the area gently with COOL water and Dawn dish soap is recommended. Warm or hot water increases absorption of the irritant through his skin so cool water is better, and Dawn is an excellent degreaser and will help remove the oils.
As far as soothing his throat, esophagus and stomach at home you can give either:
1) Pepcid ac (famotidine) at ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours
These are acid reducers and should help him feel better.
I also recommend feeding soft foods mixed with water to make eating and swallowing more comfortable. If she is refusing to eat even soft foods you can try offering meat baby foods or a bland diet of 2/3 boiled minced white skinless chicken and 1/3 boiled
white rice mixed with some low salt chicken broth to make it easy to lap up and
If he continues to not eat he should see his veterinarian for an examination, coating medication (such as sucralfate) for his mouth, esophagus and stomach so it can heal, intravenous fluids and supportive care.
He should start to eat and feel better as the burning sensation resolves but cats that don't eat for several days can develop liver disease so we do want to keep a close eye on him.
Best of luck with your fellow, please let me know if you have any further questions.