Question
we are getting the opportunity to transplant about 10 white oak trees approximately 20' in height we are wondering how far apart they should be for permanent placement and any other tips to make sure they survive.

Answer
When mature the white oak has a spread of about 50 feet so I would plant about 25 feet apart.

Deciduous  trees  may be planted either in the spring or the fall. Deciduous plants may be moved in the spring as soon as the frost is out of the ground, up until the time when new foliage is partly unfurled. In the fall, they may be planted once the leaves start to turn color up until the ground freezes.

When you want to dig up a tree or shrub for transplanting, retain as much of the root system as possible.

Older deciduous trees and all ages of evergreens, can be successfully moved only if a ball of soil is left around the roots. The exposed roots should be protected with moist burlap or newspaper or with polyethylene sheeting. Every effort should be made to reduce root exposure to wind and sun, keeping the ball as moist as possible. It's best to prepare the hole before digging up the tree you wish to move.

Size of the root ball and size of the hole:

For deciduous trees and shrubs the soil ball should be:

Width = 9-12 in. in diameter/every 1 in. of tree diameter
Depth = 6 in./every 1 in. of tree diameter

This will be a large rootball for this large a tree.
Dig the new hole twice the size of the rootball and as
deep and plant even with the ground level. Mulch around the trees with not more than 3 inches deep of organic mulch not piled up on the trunk.