To reduce the itching, oatmeal baths (or oatmeal compress for smaller spots) are wonderful.
To remove the plants from your garden or area, I'm not sure other than good gloves and strong arms to pull it. However, Ivy is a pioneer plant and usually turns up in rougher soil to prepare it for other plants to grow, sort of a "forest preparing Plant" in my mind. She has a use, even though she makes us itch!
But I'm guessing you mean for spots of itchy inflamed skin that you got from brushing up against these greenies. For that, yes, wash with warm soapy water to get any residual oil out as fast as you can from when you get "infected". (likewise, wash clothes). Once the allergic reaction starts, cool compresses of oatmeal work much better in my opinion than "commercial Calamine Lotion", and is far cheaper too.
I'm sure other wise folk her can add more remedies. I usually stick to oatmeal or "grin and bear it" because i usually get poison when I am not mindful enough of her and blindly wander into them with shorts while hiking (thus, my own fault).
That being said, I know some people have VERY strong reactions to even brushing agaisnt someone who walked near the stuff, and require more Heroic medical antihistamine meds to continue breathing. So, be careful out there.