Are there any cheap alternatives to linseed oil?
If you really, really, don't care about lightfastness, paint permanence, and brittleness, then you have a few choices out of the local supermarket:


Safflower oil
Sunflower oil
Walnut oil


Some of these have either been used historically or are becoming more common in oil paints, but will have been refined much better than what you'll get in the store. Either way, I would experiment with your paints a bit with these and see what works best and then cook with what doesn't. :)