I have only had the experience once, and I am in no hurry to do it again.
Our cat ‘Theodore’ had been poking around in the garage, and managed to fall into a 5 gallon bucket of used motor oil, resulting in a very confused and slippery, but easy to track pet.
Somehow, he kept his face out, but he was dipped right up to the back of his head.
Obviously, I was not left with a choice. It was time to act.
I would have loved to have his nails trimmed beforehand, but who wants to hug a cat that has a half-gallon slimecoat?
This leads me to what might be the best piece of advice yet offered:
If your cat has claws, do NOT leave a shower curtain on the rod.
My cat, like most cats, will flail wildly until he hooks something that provides traction, and shower curtains, even the vinyl ones will suffice. ‘Theo’ was a big boy, around 16 lbs at the time. I don’t know if there have ever been any tests to determine the load limit of shower curtain rods…but in my particular case, the cat exceded them. The ultimate outcome of his frantic attempts to get out of the tub, were me being soaked from head to toe, knocked nearly unconscious by the falling rod, with a series of bloody, oil filled cat-claw trenches up my arms and down my back, and him being subjected to ‘kitty-hell’ (I’m just talking water here, I was very gentle with him.) for over two hours.(that’s in human time)
The cat had to be washed and rinsed a total of 12 times: twice with GO-JO™ hand cleaner, 4 times with a combination of GO-JO™ and Dawn™ dish-washing liquid, 4 more with Dawn™ alone, and a couple of times with Johnson’s™ baby shampoo. I hoped the baby shampoo would leave his skin less irritated than dish soap might.
There still were minute traces of oil deep down near his skin, but I didn’t think either one of us would survive any more extensive cleaning.
All told, it was an awful experience for both of us, and I think in the future, I’ll just toss oil soaked cats in the washing machine when I’m doing my oil soaked jeans. 
For the record, I no longer store used motor oil where ANYTHING can get into it.