"Egg shaped" is not bent. That is just out of true. If there are no areas where the rims are actually deformed, such as from hitting something, then it should be a simple matter to true up those wheels. A dial indicator makes it easy, but I did it for years using nothing more elaborate than a pencil.
First get it close to round. Loosen spokes a little where the rim goes "in," and tighten them a little where they bulge out. Then when it is reasonably round, adjust the side-to-side alignment. Again, loosen spokes on the spots where the rim goes to one side, then tighten them a little on the other side.
Start over, and do it again, until your wheels are nice and true. Finish up by making sure all the spokes are about the same tension. Just go around and around the rim and tighten each spoke a little till they all feel about the same. Re-check or roundness and side-to-side wobble and make any fine adjustments that you need to. When you tap the spokes one-by-one with a wrench, they should have a nice uniform "ping." A spoke that is not properly tensioned will go "plunk."
Your only investment is a spoke wrench and some time.