pretty much every nut and seed except stone fruit pits, and olive pits. There are a bunch of vids on youtube showing coconut, hemp, sunflower and a few other oils being made. Even sorgum juice for syrup. I believe it has great benifits now and after the loss of power. We are working many things into the garden to make oil this year. Oil seed pumpkins, sunflowers etc. Might even run some hops through it.
I know for a fact that stone never needs oil to use - you can burn anything on stone and you can just wipe it off - so if you used a stone for cooking there will be no need for oil - also if your fishing, skin back the scales and the fat and juice there is an effective healthy cooking oil
(also no one really cares but if you cook with olive oil the heat destroys all the health giving properties - cooking with olive oil you should not exceed 150 degrees Centigrade )
Sunflower seeds make great oil. Grapeseeds do too. Olive oil is cold pressed, it's done with huge weights after the meat is stripped away from the pit and then squeezed out of huge rope sponges. I dunno how to make soybean oil but it's awesome too.