I assume you are asking about the Russian Olive or Elaeagnus angustifolia. This is a tough species which has been classed as invasive in many parts of North America. These plants have a good chance of a successful transplant if you take a few preparations.
You can assume that their roots will extend out as far as the branches on the leaves. At the start of the growing season use a sharp spade cut a circular trench at least six inches deep, preferably a foot, around each tree. I am assuming this will be around a three or four foot in diameter. Water in and wait a month. On transplant day water in the plants and start digging.
Considering the tough weedy nature of this plant you could just take your chances and dispense with the preparations and dig them out now. Another approach that involves less work is growing them from seed. With their rapid growth you could have a good hedge with less work in a few years.
I wonder if you would consider planting a native species instead of the Russian Olive? The yaupon and sophora are local and make a good hedges.