Q:

How much weight will a 4"x8"x20ft oak beam support?

I am building a tree house. I will cut two support beams from oak to support the building. How much weight will a 4"x8"x20ft oak beam support? 
I will be working between two trees. 

A:

The strength of the wood beam will depend on the specific species of oak, the grade of lumbar, whether there are any cantilevers, side bracing, and other factors. But 20 ft seems like a very long span for a 4x8. Glancing at some load tables I would say you're in the ballpark of only a few hundred pounds capacity, which is not sufficient when you take into account the weight of the structure, the weight of occupants, snow, etc. (Don't take my word for it: you must get a more accurate number before you start building). (By the way, where are you going to get a piece of solid oak that long??)
Another side note: you don't say anything about the design of the tree house but be careful about how you connect the trees. When the wind blows the trees will move independently and you need to make sure that your structure isn't rigidly fastened to both trees. There are many examples online about how to make a platform that is fixed to one tree and slides at another. If you don't allow for movement of the trees you risk damaging the treehouse or the trees themselves when a gust of wind blows.

