I think you better keep a close eye of him or put him out in the yard. I think you are going to see that coming back up or out the other end fairly quickly. It should not hurt him. Where was the cooking oil that the dog could get into it?
My dog drank 2 cups of oil that fish was fried in what will happen?
You should take him to the vet to make sure that he isn't going to get very ill from this. Hope this helps.