A pressure gauge would be interesting. http://www.homedepot.com/p/Watts-3-4...IWTG/100175467 http://www.homedepot.com/p/Rain-Bird...-P2A/100575619
Connect it to the faucet on your laundry tub or washing machine hot tap. I don't know what temperature the gauge is good for, but if you don't run the water, things should stay fairly cool at the gauge. The point is, does your pressure rise a lot when the water heater goes on? What pressure is present on the hot water when your relief valve leaks? You might just need a new relief valve.
You might need an expansion tank. The gauge will be informative.