Which kind of tool can be used to spread one oil pastel colour over another? For example, I colour a leaf green with the oil pastel. Then I want to spread 
that green colour of the leaf edges, outside. For this, I use my thumb. I put my
thumb on the leaf edge on the paper and them push my thumb forward.

This works, but it also make my thumb dirty. It also means that I will have to wash my 
thumb with soap every time I want to spread a different colour. 
Also because my thumb is big, I cannot spread colours of small areas effectively.

What are my options?
One way to simply keep your thumb clean is to wrap it in a paper towel or cloth. This doesn't really resolve the problem of thumb size, however -- indeed, it makes your thumb larger.

For finer detail work, a tortillion would be better. This is a rolled-up piece of paper that tapers to a point. This is much like Zizouz212's suggestion of an eraser, but perhaps less expensive -- you can purchase tortillions, but it's also possible to simply roll your own from whatever paper you have on hand (here's one tutorial).