Getting rid of the problem, doesn't sound easy. According to the University of Ohio website, it can take up to 4 years to eradicate the beetles. The suggestions are to use a spray, hand pick the beetles,cultivate around the affected plants and use Japanese beetle traps.
My experience with the Japanese beetle traps is that every Japanese beetle in the neighborhood ends up in your yard, because the traps have a mating scent that attracts them.
To make hand picking easier, use a bowl of oil and knock the beetles in it. If you don't want to touch them, use a pencil or something. This can take awhile because the bugs fly away when you get others in the oil.
Cultivating around the plants is suppose to help kill the larvae in the ground, so you'll want to do this before they hatch.
Sprays recommended can be found on this chart.
I'm sorry to hear you have this problem. It is also suppose to affect grape vines. I know what a challenge Japanese beetles were here at one time.