How do I treat green fungus on my aging piney oak tree?

The fungus you are referring to may actually be Lichens that are growing on the tree. This will not harm the tree if that is the case. Lichens are actually a sign of good air quality. The smaller branches that are dying back may be smaller limbs that are being shaded out by the canopy on the interior. Some small branches are somewhat expected. It is hard to answer this question without looking at the tree. Make an appointment today to have a certified arborist come to your property to inspect it further.