Can plastic grocery store misters be used for oil?
No, they don't work well. I've tried them. 

First, the viscosity of the oil seems to be wrong for them. Instead of producing a cloud of oil particles, they produce a stream which exits with some force, like a mini water pistol. Second, the plastic of mine got softer with time, and I had the feeling that it also lost some color, so I suspect that something from the plastic leached into the oil. 

It might be that I had unusually bad luck with mine, but I suspect that the physical properties of oil and water require different pump head parameters and the problem will apply to any water-intended model. If you are really strapped for cash, it makes no sense to make such a risky investment, since the chance it will work is not good.