I've done it both in the fall and spring. I tend to have more luck in the fall. I'm from Raleigh. The first couple shovels in the ground are the most important. Make sure you don't dig too close to the tree as not to cut off too many lateral roots and dig deep as oaks and many other trees have pretty long tap roots compared to their above ground growth. Don't add potting soil to the natural soil...but organic material is ok as long as it's not all you back-fill the hole with. Good luck.

Whether the trees are worth moving is more of a judgement call than a matter of fact, especially without more info/pictures. You are in a better position than any of us to know whether your effort and these particular trees are worth moving. You might also weigh the possibility and benefits of purchasing nursery stock for the project.

As to how to move them, here is a link to a set of instructions that should answer most of your questions about how to move them:
sites.google.com/site/tnarboretum/Home/planting-a-tree-or-shrub
and here is a guide that can help give you some idea of how much rootball would need to be moved:
sites.google.com/site/tnarboretum/Home/generic-rootball-size-guide

As JQ said, you may want to go a little deeper than the guide shows for the the oaks, but don't expect to get even most of the taproot.

I generally do not recommend adding amendments to backfill. Adding more than 5% organic amendment (or other amendment, for that matter) to the backfill is almost never beneficial and is frequently detrimental to the optimal establishment of woody plants.