A combination of beating it down hard and then covering it with wood chips will do the job. You will need a lot. Ivy and those other plants are all hard to kill.
Beat them down to bare earth with a mower/weedwacker/tiller/hoe/hogs/whatever, then cover deep with wood chips, at least a foot deep, and make sure you go all around, beyond where you think the edges are.
Keep an eye on it, and if anything green ever shows itself, rip it out and dump an extra foot of chips all around. In my
experience poison ivy can come back the following year, from
energy stored in the
roots. So keep it covered deep all through this summer and winter, and past next year's growing season.
Some people use black tarps with the sun beating down in the heat of summer to bake the ground. This can work, but you need hours of direct hot sunlight for several weeks. If you have this, you can do it faster. But wood chips will improve the soil for long-term health. The black tarp method is more like a quick fix to kill everything.