EEEK! The reason why the Tide works is because it literally chemically burns your skin overriding the itch receptors!
What causes the itch in poison ivy is urushiol which is oily. A quick fix for the itching is 1 tbs of bleach to 1 cup of water. That will break up the urushiol. Dab it on the affected area. Once the itching stops, rinse the area with water, pat dry with a paper towel but do not rub the area. Then dab on some calamine lotion.
All clothes that have been in contact should be washed separately with bleach and all garden tools should be wiped off with a half and half solution of bleach to water.
If you know you are going to be working in an area with poison ivy you can spray the poison ivy with a half and half solution of bleach and water - it will neutralize the urushiol on the leaves. Just be careful not to get it on plants or grass you like as it will also start to kill the poison ivy.
A good way to kill poison ivy is spray the leaves with bleach full strength. Now before someone says EEK that's bad for the ground, it isn't. Once bleach dries it become inert, even after an area cleaned with bleach gets wet again.
I am one of the lucky people who do not react badly to urushiol producing plants like poison ivy or poison oak. I guess that's why I always get volunteered to remove it.