This is the method I've used since I was a child to relieve itching from poison oak. I think it will also relieve itching from poison ivy and maybe poison sumac, but I've never been exposed to those, so I'm not sure. It also works to relieve itching from mosquito bites.
Note that this is not a cure for poison oak / poison ivy / poison sumac - as far as I know there is no way to actually make the rash disappear once you have it, except waiting for it to heal and caring for the skin. But this does help to relieve the itching.
WARNING: the method described here works great for relieving the itching once the poison oak rash has already shown up and started itching like crazy. DO NOT USE THIS METHOD THE DAY YOU ARE EXPOSED TO POISON OAK. When you are first exposed to poison oak, the most important thing to do is wash the exposed area with detergent soap and cool water as soon as possible to break up the plant's oils and remove them from your skin. The quicker you get rid of the oils, the less they will spread and the milder your rash will be later. NEVER USE HOT WATER RIGHT AFTER EXPOSURE TO POISON OAK. Washing in hot water causes your skin pores to open up and when you have fresh oil from the poison oak plant on your skin, the opening your pores will just let more of that oil in and your rash will be worse later. So if you just fell in a poison oak bush, stop reading this now and go wash off with cool water and soap. Then come back here in a couple days when the rash shows up.
Step 1: Apply Warm Water
Uncover the skin that has the rash and find a faucet in a sink or bathtub.
[REMINDER: DO NOT DO THIS IMMEDIATELY AFTER EXPOSURE TO POISON OAK. THIS ONLY WORKS LATER ONCE THE ITCHY RASH HAS ALREADY STARTED. DO NOT USE HOT WATER TO WASH OFF POISON OAK OILS FROM YOUR SKIN.]
Okay so you have a poison oak rash (or mosquito bite) - this can happen to the best of us. The easiest place to use this method is in the bathtub before your shower. Put the affected area of skin under the faucet and turn on some warm water (not hot) and let the water run across your itchy patch of skin. You're going to be here for a couple minutes, so get comfortable.
Now you're going to slowly turn up the heat, a step at a time. You want to turn it up just until it's hot enough that it will make your rash itch a LOT. As soon as you get to that heat where it gets super-itchy, stop turning the water up and just let it run over your skin. This will feel itchy/scratchy/wonderful. The stimulation of the hot water feels like you are scratching the whole rash at once. (But don't actually scratch it!)
Now after a little bit - maybe 30 seconds - that wonderful feeling of the relief you get from scratching will go away. Now just nudge the water temperature up again to be a little hotter. The feeling of scratching the whole rash will return. Enjoy this until it goes away.
Step 2: Gradually Increase the Heat
Keep nudging the heat up gradually like this with a small amount of water flowing over your rash. You want enough water to heat that part of your skin, but you probably don't want the faucet on full pressure, spraying hot water everywhere.
Each time you increase the temperature by a step it should feel like you're scratching your rash. You'll feel that rush of sensation as if you were scratching the poison oak. Turn up the heat a bit and WAIT. Enjoy the sensation and wait until it has gone away. Then turn up the heat again.
Eventually after a number of times nudging the heat up a notch at a time, it will be very hot. DON'T BURN YOURSELF. IF IT GETS TOO HOT, STOP. But do use the hottest water you can stand without scalding yourself. This will give that same satisfying feeling you get from scratching.
Once you've gone through this routine, turn off the water, dry your skin off, and go about your life. Your rash should not itch for several hours. I don't know the exact physiological reason for this - someone can probably write it in the comments.
Thanks for reading and have a less-itchy day!