If you can wait until fall to transplant them, it would be advised to do so in order to reduce the transplant shock.

Azaleas can be transplanted. They have wide but shallow root systems. I'd suggest pre-digging the new hole before moving them. Slight amend the new area with composted pinebark (sold as nature's helper or soil conditioner in bags at HD). Mulch well to retain water and treat them as newly planted for the first year as you would any purchased plant.

If the construction is going to take place before Fall, go ahead and move them. They can be moved any time they are not in active growth (the period immediately following bloom) or the ground is not frozen -- IF you are prepared to be diligent with water. If there is considerable sun in the new site and the weather is warm, you may also have to provide some temporary shade for a few days.

You can assume the roots extend out as far as the widest branches, but you can take a smaller rootball if necessary. Aim for a diameter equal to 2/3 the plants height. Drag on tarp or cardboard rather than carry by the stem to their new site. If the new site has been recently spaded, allow for some settling of soil, you don't want these to end up lower in the ground than they were previously planted. Mulch, keep moist.

Great responses! Thanks very much.

In addition to what already said, if you have a luxury of time and could wait till spring, you could root prune them now i.e. cut around perimeter of your future rootball, but do not remome plant from the soil.
Azaleas will try to reestablish lost root mass in current year thus will have a better start the next one, when you transplant them.