Yes washing clothes (hot or cold) will get rid of the urushiol oil. Urushiol is easily washed away using soap and water provided it hasn't bonded (ie like with your skin).

There are many ways to get rid of those pesky ever returning plants. Some techniques work quickly and others take time. I've been pulling at a poison ivy plant mixed in with an old azalea bush for about 7 years now. I think last year's hard work paid off as I can't find any evidence (yet - I've got my fingers crossed) that the plant survived. I just kept pulling at any vine that I could find and dug as much of the root up as I could. year after year until gone.

If you are not attached to your bushes (as I am) then pulling them up and spraying with Brush B Gone is a good idea though perhaps a bit more drastic than necessary. My husband uses Round-Up on the poison ivy plants and has had some success in keeping it at bay and even eradicating it amongst some of our bushes. The key to killing poison ivy is making sure you get the root otherwise it will keep coming back. One year, I painted either Brush-B-Gone or Round-Up (sorry I don't remember which) onto the roots after pulling up the plants. That helped alot.

The poison ivy berries apparently are a tasty treat to birds and other wildlife. I've had poison ivy plants show up in places I didn't expect and assume its due to the birds "depositing" the seed after munching on the berries in a totally different location. Also, PI puts out runners - sometimes VERY long runners. Everything I've seen has run close along the ground through the grass, etc. It may be that you don't see the vine as its hugging the ground so well. Or it may be that you have a number of presents from your various wildlife friends. You might want to help eradicate the neighboring PI after getting control in your yard to help save you in the future.

Good Luck!