My reliance 501 is leaking at both entry hoses ports and also is very hot to the touch near the electrical connection port on the top of the water heater.

SOURCE: need to empty reliance 501 hot water heater how?

1) Shut the breaker off to it at the panel. 2) Hook a hose up to it (the bottom has a drain). 3) Close the valve to the water heater (on the cold water supply). 4) Open drain on the bottom of water heater. 5) Open the relief valve to allow air into the tank (it won't drain otherwise - think if you put your finger on one end of a straw - the liquid stays in until you let go). Why are you draining it by the way?

SOURCE: I have a reliance 501 electric hot water heater

it is located on the thermostat. Take the cover off the side and you will see a little red button in the side of the themostat.

SOURCE: Reliance gas water heater 40 capicity, has a leak on the top

Most likely only one of the pipes is leaking but weaping enough to cover the top and indented places near both inlet and outlet. This leak has most likely penetrated all the insulation and is a problem throughout the tank wrap insulation...If you are able to blow air continuously long enough to determine which connection is leaking then fix it. It will likely to take quite a while to dry out all the insulation if the water has migrated down into the tank wrap... If you determine that the insulation is waterlogged, you may be able to drill several small holes in the external cover.
good luck

SOURCE: I have reliance 501 electric hot water heater, and

There is an address near the end of this link to request manuals of reliance water heaters not listed. http://www.reliancewaterheaters.com/lit/om.html
it is quite possible that your heater works on the same principle as one of the other models and just differs in capacity or power rating.

SOURCE: 1992 Reliance electric water heater model 501 has

Check the breaker and top thermostat and make sure they are not tripped. Move onto replacing elements if above is not the problem.
Turn water and power off to heater and attach a water hose to bottom of heater to drain down tank. May have to open hot side on a facuet to get it to drain.
Once drained remove elements with 1 1/2" found at local hardware stores. once elements removed and new ones in place. Turn water on and get the air out of the system. Once water is flowing from the hot side from all of facuet's in house.
Once all air is out now yaou are resady to turn power onto heater.