I am using green oak timber - primarily 8x8's for posts, girts and rafters. My problem is the timbers are not true to the stated dimension and very often have significant bows and or twists. This throws everything out of square. If I make my joinery square, dimensions don't work. If I go by dimensions it's rarely square. Do I have to just try and make a compromise between what is right dimensionally and what is square?

Specifically my roof is a 12 -12 pitch. If the tongues and fork at the peak is square, the bird's mouths on top of the posts are way off because of the bow in the rafters. Bow is always up.

Sounds like a perfect application for square rule joinery. Jack Sobon's two books on timber framing provide the most coherent and user friendly explanation of the process that I have seen. The basic idea is to work to an imagimary square timber (say 7.5" x 7.5") inside your bowed 8x8. The timber is reduced as needed to 7.5x7.5 in the area of the joints and the joinery is then cut. You calso end up working off of a snapped chalk line to establish "straight."