If the nut holding the main pipe leaks oil, the nut may be loose or possibly the ring on the pipe and seat on the threaded section which it tightens against may not be mating properly. It's worth trying to clean the surfaces with a plastic scouring pad or rough cloth to see if that improves the situation. Abrasives should probably be avoided to avoid damaging the surfaces. Possibly Evo-Stik Plumbers Mait or similar would help to seal the threads.
The leather washer on the pump had dried and worn out so it needed a replacement. Finding parts for a blow torch such as this was out of the question so I decided to make one. I tend to be a hoarder and lots of stuff gets sorted and stored which should be thrown out! However the parts do become useful when something needs to be repaired, and it saves money. Leather is a very tough, durable material and can be used for making washers and gaskets. It's not totally waterproof (think of how water soaks through your shoes) but does stand up to high temperatures and doesn't melt. I used a piece of leather from a shoe to make a part for the pump. It needed to be reasonably thick so that it bulged out during the downward pump stroke and relaxed during the upward stroke.