I've used my food processor and my nutri-bullet both to make "nut butters". Nuts have plenty of oil in them, you just have to be patient to coax it out and get them ground to the right consistency.
It takes some patience, and I'm probably over-cautious, but I don't let either of the grind like mad for the entire time. I grind for a bit and then let them rest. =P And then repeat often. It always seems like when I'm just starting to wonder if I bought a bunch of dud nuts that won't work ... it magically starts to come together.
My favorites are cashew. And sunflower seed. But every kind of nut will work.
If you're out of tahini and are hankering for some hummus, grind a couple tablespoons each of sesame + sunflower seeds in with the garbanzos, they're the perfect substitute. (I've never tried to just grind sesame seeds, I'll have to try that!)
CharlieD - I love, love La Tournagelle oils. Their walnut oil is my go-to for topping salads and it most definitely has a roasted, toasted walnut taste. I know they do a Sunflower oil, but I've not tried it; it may be worth finding.