I guess they're still making pumps with oil, but it's been a long time since I've bought a pump, I wouldn't know. If it is oil leaking from a pump, you'll know shortly, as they tend to die soon after that starts.
Oil from chainsaws used near a pond could cause a slick, but it really isn't all that likely unless they did something really stupid. . .
Most Koi foods do contain fish oil. Some of the less expensive ones (actually re-labeled cat fish food,) contain a lot of it and will leave a sheen on the water. Nice for feeding algae blooms.
Decompositon of any organics will also do this. Anything from fish to frogs, to plant parts. This is also a common cause of a sheen on the water.
Mike S.
Spring Hill, FL