Please do not try to use all of these methods at the same time. Pick one that suits the project you are doing.

1)Use white glue and let dry between coats. 5 coats for chicken eggs. 3 coats for goose eggs.

2) One coat of Envirotex Lite is equal to 50 coats fo polyurthane. It is messy to use, but gives you a high gloss finish.

3) Use half and half of white glue and decoupage medium.

4) Use gesso on the inside of an egg. Use the spray gesso on the outside of an egg.

5) If you just want to strengthen the eggs, try TLS, or Tranluscent Liquid Sculpey. Its available in clear, black, silver and gold. Its a thick liquid that can be painted onto the shells, then baked. It keeps them very light weight, but also very much stronger. (from Sarajane)

6) This can used on the inside of an egg to add strength.
Golden Gel Mediums Hard Molding Paste
Golden #3571-5
NET 8 fl. oz. (1/2 pt.) 236 ml
Made in the U.S.A.
Dries to a hard, opaque film. Excellent for building surfaces, creating texture and carving. Easily sandable. Avoid use on flexible supports.
by Golden Artist Colors, Inc.
New Berlin, NY 13411 U.S.A.
607-847-6154
www.goldenpaints.com (from Lee Boyle)

7)Strengthen it with Durham’s Water putty. This can be found at your hardware or home improvent store. (from Terry)

More on Durham's Water Putty.(about 3 parts powder to 1 part water). It should be a thick consistency but you should still be able to pour it. I also like to use water putty to strengthen the inside of the egg. Use the same method, just mix enough to cover the interior. Pour out the excess. The drainage hole is filled automatically because some of the excess settles at the bottom. It thickens the wall, makes it inflexible and can be easily painted. You can also cut through it. It's especially good when used in musical jewel boxes to add strength where the egg is handled most.
For carved eggs, use the water putty, let dry, then carve.
I've used water putty with great success on all kinds of eggs, including delicate eggs such as quail eggs and chicken eggs. It costs about $2-$3 at Home Depot.
(from Jean)

8) For eggs which I'm not going to open, I'll use either silicone caulk to close up the hole, or Great Stuff insulation foam (very carefully!) (from Jean)

9)J's Complete Coat for strengthening and sealing eggs.