Only seven months old. Kenmore. No problems until about a month ago when a day here or there, in the middle of the night, we would hear water in the pipe nearest the water heater and then a loud shrieking noise and thump. This also would rattle the pipes. Loud. We have a small home and it would wake a few of us up. Couple times a night at first, then steadily worse.

We called Sears who sent out a tech. He did something with the burners and tightened a few screws, all under warranty. His assistant tech chimed in that the new water heater chimney is too large for the 3" pipe it attaches to, that he felt this was the problem. But the tech felt if that was the problem why were there no problems for the six months prior to the problem manifesting itself. Whatever they did? It didn't work. As of last night it was WORSE, once every 6-10 minutes from 2am-5:30am, then intermittent until 7 or so.

Any ideas? A new tech is due out tomorrow and I would like to have some concept of what might be happening because I averaged 3-4 hours of sleep all week this week! Help!

Sounds like water hammer
Have a repair guy address this as a solution for you

Have the water pressure tested
And the temperature of the water when it is done heating
More temp the water is ,the worse the pressure and more possible noises

The only logical way for a water heater to make a shrieking noise would be if the T&P valve release because of over temperature. That is releasing steam, it could make a noise just like a steam whistle. If it released for pressure it would be releasing water and would not make any noise. The thump would be the T&P valve closing.

Hi Tomy and Welcome to The Plumbing Page. At AskMeHelpDesk.com. I would have bet that this was a gas hot water heater even before I read it in Tonys post. I'll also bet that Tony doesn't flush out his water heater on a regular maintenance schedule.
If you do not flush,(not drain) your heater on a regular basis it will build up mineral on the bottom of the tank. When the flame comes on it turns the water trapped under the mineral to steam and the steam escaping is what you hear. Let me show you how to flush your heater. Attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run until the water runs clear. You will see a spurt of red,(rust) and some white grains,(lime or calcium carbonate). The whole thing shouldn't take more then a few minutes. Don't forget to flush it out every month. Your heater will thank you for it. You might want to consider cleaning the screens on your aerators if you have a high mineral buildup. If the problem still persists after you have flushed, you will have to drain the heater, remove the boiler drain and go up in the bottom of the tank with a wood or plastic rod, (not metal) and try to break up the mineral and flush it out. Good luck and thank you for rating my answer, Tom