Poison Ivy has both pros and cons. It can be a major food source for your winter birds as Cardinals as well as providing very safe nesting areas. After it blooms in mid-summer it creates tightly packed clusters of white berries. Those berries need several good freezing and they are ready for the birds to eat.
I have one patch that must be 30 years old and the main trunk is about 2 1/2" in diameter. It took over one of my smaller white pines and reaches well above 8 - 10 foot off the ground and spreads along the adjacent fence line for another 10 foot or so in both directions.
Now ... I am one of those 'back to nature hippie freaks of the 60s' and live on 3 1/2 acres of old farm scrub ground. So for me to give up some of my fencing to poison ivy is no big deal.
All parts of the poison ivy plant have toxins - stems, leaves, flowers, and berries. But it seems that as it nears flowering is the worst time and mid-winter when it is dormant is the least toxic.
I might suggest that you get some black plastic at your local hardware store, some heavy brown jersey gloves, a small real of 18 gauge fence wire, heavy wire cutters that are sharp (don't trust the ones in the bottom of the tool box), scissors, a nice stack of old newspapers, and the garden hose. Put on your knee high socks, and your long jeans with a simple rubber band around the leg opening to keep the pants closed.
Open up the newspaper and throw down a nice layer on top of the ivy. Wet the newspapers thoroughly. If you can put on a second layer and water it too. Now cover that with a couple of layers of black plastic. Cut 12" pieces of fence wire, fold it over in half so it looks like a giant hair pin with a 1" or so curve in the center. Push the wire pins, along the edge of the plastic, into the ground to hold the plastic down during storms.
Now wait ... GRIN ... as the summer progresses all that water you poured on the newspapers will get extremely hot under the plastic and literally burn out the root system. No sun, so no leaves and no new growth, burned up roots = dead plant.
Then around mid-January, when you are going crazy with a bad case of cabin fever go grab the rack, hoe, and those brown jerseys and uncover the patch for clean up.
Simple, safe, and right down to the roots without any chemicals !
Oh! And after each gardening session wash your brown jerseys in some good, strong lye and lard soap!