There's no doubt that Oyama Sosai was a naturally gifted fellow. He wasn't by any means, a lightweight, and had a larger frame on which he could build that the "typical" Asian.
Natural talents can take you a certain distance, but in Oyama's case, he would put himself through a gruelling workout routine that kept him in tip-top shape. If you look at some of the pictures of him, he is a rather impressive physical specimen.
I suspect that his pain receptors were rather dull compared to a normal human being's. Given all of the full contact hits he took throughout his life, it wouldn't have been surprising to see the condition of such nerves, if they even existed anymore. That might explain why he was able to tolerate extremes that ordinary folks couldn't.
Combine all of the above with a strong mental discipline, and that could very well give you an answer.