You have clog in the water line.
Since all hot water pipes are involved, clog is probably near water heater.
Buy pressure gauge at hardware store that threads onto hose connection. Brady BTG 100 at AmazonPicture of gauge
Check outdoor pressure for baseline pressure in your home.
Turn off electricity to hot water heater for an hour or two so there is not scalding water.
Open drain valve on water heater to see if water heater is clogged with sediment. http://waterheatertimer.org/Water-heater-will-not-drain.html
Put pressure gauge on drain valve and compare with outside pressure.
Open hot water spigot on bathtub and see if tank pressure drops ... if tank pressure drops significantly with bathtub spigot on, then clog is on incoming cold water before tank, and could be on outgoing hot water pipes too.
If tank pressure stays about the same, then clog is on outgoing hot water pipes.
Clog can be sediment caught in cold water shut off valve located above tank. Open and close valve and test pressure again. Take apart incoming cold water pipes above tank and check for sediment. Replace valve. Look at condition of cold water nipple on top of tank.
Sediment caught at hot water elbow near tank.
Sediment can fill up old pipes. Take apart hot water pipes above water heater and see condition.
Look at condition of hot water nipple on top of tank.
You may have to take apart pipes up to first or second elbow.
Pipes can decay at joint where copper pipe connects to galvanized pipe. Check for copper to galvanized connections on cold or hot pipes and replace section of galvanized pipe. Copper pipe will probably be good, the galvanized pipe will deteriorate. Replace copper-to-galvanized joint with 3/4" non-conducting union from hardware store