How can I get rid of poison ivy and poison oak?

They sell a spray especially formulated to kill this.

Cut at the root and apply herbicide. Once it has withered, you can remove the vines more easily but they can still produce a rash so continue to wear protective clothing.

How much do you have? This is for a small amount, not a field of it:

Since I can’t yank it out (allergic) I would mix up a small batch of herbicide in a clean used plastic cup or “tin” can.

I’d apply it with dollar store kids’ long handled small paint brushes to the middle of where the 3 leaves meet and leave a big droplet there. If you can paint the leaves a bit then great, but I keep my time near it very short.

Of course wear long disposable dishwashing gloves, long sleeve shirt, long pants and tie the hair back.

Throw away the gloves when done, taking care not to touch the outside of the gloves.

If you brushed against the plants with your clothes they will need to be washed twice with lots of soap & lots of borax. I would wash mine in a commercial washing machine, because they get hotter water.

If you are looking for something natural, try this

https://countrylivinginacariboovalley.com/homemade-poison-ivy-and-weed-killer-that-really-works/

Hey Cal: Get a product called ground clear, it kills everything! You can get it at most home improvement stores. Then, put some in a small can and paint the undersides of the leaves with this, using a small foam brush. Be sure not to get the ground clear on anything else. The plant will take the poison to the roots, through the leaves, and kill just this plant - if, you are careful not to get the ground clear on anything else. You can use this method on any plant you want to get rid of. If you are worried about the leaves touching your other plants, cut the unwanted plant short, leaving several leaves, paint the leaves with the ground clear and then cover it with a plastic bag and secure it to the ground with dirt or rocks. That way, even the wind won't blow the poisoned vine onto your other plants. Good luck with this, invasive plants are the worst!

If you are, or you know someone who is, diabetic, ask for one of their used needles, fill it with the ground clear and inject it, in a downwards direction, directly into the vine. Then, be sure to dispose of the needle properly and don't touch the needle part because you may get some of the poison ivy oil on you. Good luck