Those are all poison ivy. And big healthy established vines by the look of those blooms! What a job! If it were me, i'd don heavy duty protective gear in 2-3 layers(preferably an outer layer you can toss afterwards), and start cutting away as much as i could while it's dormant and fairly easy to work around. That won't kill it- but when it reprouts at the ground where you cut it off you can hit that with roundup and not damage other stuff. If someone in your family is more resistant to the oils, let them tackle the job. When you're cutting big vines especially, do it slowly so it doesn't splash/squirt sap around. Probably a good idea to wipe down your pruners as they get wet, too. Not sure how 'juicy' it'll be this time of year- i know at other times, the big vines are pretty sappy. It's going to be awfully hard to spray it thoroughly and not get anything else if you don't trim some of it down. You're taking some of the plant's system and weakening it some by trimming. Plus, it takes more spray if you leave it as it is than if you trim. Best of luck! As others have said- be very careful, and wash with technu really well afterwards. If you do end up with a rash, zanafel works pretty well at reducing the time you have it (it's expensive, though). There are a couple of prescription creams that will help tremendously in drying it up as well, and they aren't commonly known. The steroids and shots do work, but i don't like dealing with either one. The dormant vines can still give you a whopper of a rash, and the sap is the worst. If it were me, and this rental had it before you moved in, i'd ask the landlord if they'd knock off a little rent or pay for the weed killers for you. It's a nasty job, and you should get some compensation.

I was going to mention virginia creeper also. It has leaves in clumps of five and is often misidentified as Poision Oak. Even though I try to be organic as much as possible, I will break out weed killer (Ortho Brush B Gone) for Poison Ivy in certain areas. I am very allergic. I've tried cutting it off, but invariably it gets on my tools or my clothes or my dog and I end up getting a severe (and I mean hospitalized for blood poisoning) rash. So I let it be, if its growing in areas where I won't be in contact with it. But if it creeps up my shed or a tree in the mown area of my property. I take off my organic hat and put on the chemical one.

leave of three for PI .. leaves of 5 for this bird spread nightmare ... lol .. that sprig can grow 5 to 10 feet this year ... its just fine in the woods ... but not going to be great.. in your garden .. ken

come on janny ... leaves of 3.. let it be.. leaves of 5.. who cares ... its very clear in each of your pix ... we are glad to verify whatever you determine ... but you have to learn and take that leap of faith ... that you can do it without us ... next post ... you give us your guesses first ... so we can grade you .. lol ... just dont stop posting ... if nothing else.. this is a puzzle forum ... ken