Never heard of giving oxytocin to a non lactating animal that does not give birth to live offspring. Oxytocin has 2 main actions. Causes contractions of the uterus to assist in birth and the let down response in lactation.
We ended up taking our hen to a vet yesterday. He took x-rays (yes, we love our pet hens) and found at least three "eggs" inside. She has been stumbling around quite severely for two days. We have her in a cage in the garage. Otherwise, she seems healthy. The vet did give her an oxytocin shot to try and help expel the eggs. The other thing he said they could do is to draw the fluid out of the eggs, although I'm sure that is expensive and sounds dangerous anyway to me. Our hen has not laid these eggs. I was wondering, since the eggs, from my research, would indicate they are laid in the abdomen and not the oviduct, how the eggs would even be expelled with contractions since they're not in the oviduct (at least my understanding. He did not say that though, but just that she was laying internally). I'll keep you posted if she ends up laying these eggs or not, although I would expect her to have laid them by now. It's been about 18 hours.
