I had a rod stick together once. It wasn't caused by oil though, it was just stuck. I applied really hot water with a rag to just the bottom (female) half of the joint, thinking that it would expand quicker than the male end,...and it worked! Took a few minutes to heat up but I could feel it loosening up as I was twisting on the top piece and then it just slid right out.
But....this wasn't a real expensive high end rod so I would be really careful in your situation and I don't want to be responsible for any damages, so my advice is do not listen to me. (my legal disclaimer )