I'm having a problem where the how water is sputtering out of faucets and making a loud "jerking" noise from the hot water tank area when the washer tries to pull in hot water. I tried releasing the pressure relief valve on the hot water tank which hadn't been done in a while but did not seem to do much (on a side note, even after doing this about 5 times in a row the tank continues to drip for days now which I can't seem to get to stop). Please advise.

Does this only occur when the washer is being used?
Leave that pressure release valve ALONE. It is release valve, not a drain valve. It sits there for years doing nothing. Mineral deposits build up around it, you open it and mineral deposits get caught between the seats and washer. Then it won't completely seal, as you can see. Now you are going to have to replace it.

The loud noise by the hot water tank only accurs when the washer is on but the occasional sputtering can occur at any faucet when the hot water is turned on. Regarding the release valve, I was told that you must clear the valve at least annually.

Sounds like you are getting "water hammer" caused by the abrupt closing of the washer fill valve. This causes pipes to vibrate and bump against something. You can eliminate this by installing a air chamber. You can purchase one or you can make your own. Cut the line and install a "T" fitting with the center outlet pointing straight up. Then install the purchased air chamber or install a 14" to 16" length of pipe with the other end sealed with a cap. This will have air trapped in it and cushion the change in water pressure when the washer valve closes.

I think you misunderstood what you were told about the water heater. You should drain you water heater annually to remove mineral deposits settling in the bottom. This is done by the drain valve at the bottom of the tank. Leave that pressure valve alone.

If the sputtering at other faucets is confined to the hot side only, I think you have a loose washer in the shut valve on the cold water input line to your water heater.

I have recently installed a tankless gas water heater. When using the shower the hot flow is too hot and when I adjust with the cold the flow is too low and shuts the hot off. Will installing a 50+ gallon holding tank in the line before the hot water heated help to increase the flow?

Bred, you are clearing the wrong end of your heater. The valve you need to open once a year is at the bottom of the tank. You are touching the PRV and Harold gave you the correct info, leave it alone. If it is leaking you may be lucky and able to clear it by opening and closing the PRV 5-6 times in rapid succession. If it leaks after that you are off to the store.

Uncbob, please start your own new post rather than jumping on someone else's, it confuses us old guys. By the way, the answer is no.