If you think you have been exposed to poison ivy, as soon as possible, take a top down shower using...
as cold water as possible, warm to hot water makes the pores in the skin expand,
use a basic dishwashing liquid such as Dawn, AJax, etc., avoid dishwashing liquids with skin conditioners,
soft wash cloth or sponge, something that helps create a bunch of suds without abrading the skin,
wash, do not abrade the skin.
wash all of your body, top down, never go back up
Rinse, repeat. Might use warmer water second time around, especially if sweating or working wet.
Dry off.
Many dishwashing liquids contain ammonia, if you are sensitive to ammonia check the ingredients.
It takes time, so take your time and wash throughly.
Drink some water, make sure to keep well hydrated. Not a time for alcohol.
Wash all affected clothing with hot water, detergent, no fabric softener. Rinse and repeat. Most washing machines do a poor job of rinsing so if an extra rinse per complete cycle is an option, use it. Do not use extra soap as it will not rinse out.
You are trying to remove a thin oil residue from your skin and clothes, without doing additional damage. Be careful of over scrubbing, abrading, scratching and or drying out the skin. Try not to get any additional cuts or scrapes until you are past the normal reaction time.
Burning poison ivy is extremely horrible, do not do it.
I would cut those vines with a large pair of lopers in two places at least a foot apart. Pull the vines off next winter. I do not use saws or striking tools because of splashing and dust. You do not want to breath the dust or aerosolized oil, let alone get it in your eyes.