I bypassed the water softener. Called the water softener people and they came out and put a chemical in the resin to kill bacteria but did not believe the softener was the problem. Recommended remooving magnesium rods from water heaters. I bought the tools to do this but couldn't budge the fittings on top. Called a plumber. He came out - looked it over - said it would be cheaper to replace the water heaters than to replace the rods. Suggested I get my water tested. Why? I know I have sulfur! I drained the water tanks (2) via garden hoses and opened all of the faucets, showers, tubs, throughout the house - inside and out and ran them for half an hour. That fixed the problem for about 10 days. Now the problem is back. I do not have a pre-filter. Someone suggested chlorinating the water lines. How would I do this? Who do I call next?

It does sound like it is the anode rod in water heaters. I was the one that suggested chlorinating house. Pulling anode rods can be a pain in the!! As you found out. It is not cheaper to replace water heaters and the same problem will occur. Your water softener company should be able to remove the rods, chlorinate water heater and flush tanks afterword.
RJ