What are the advantages of using dead wood to heat a home compared to using fuel oil as far as global warming?

Agreed with a couple of previous answers. If this is wood that would have decayed anytime soon, or from a sustainable harvest or thinning operation (that will enhance the growth of other trees), then it beats fuel oil. If you burn it dry and efficiently (like in a newer high-efficiency stove), particulates shouldn't be a big problem.