We do not have them out here (Thank goodness) but I would combine traps and spraying or baiting. Anything, as long as the timing is right. If you can get them as they come out of the winter they won't build up as much or as fast.
If you miss the timing then the population has time to build, then it can make it to the stage of laying eggs for next year's beetles.
The first part of the control is a disease that is specific to Japanese Beetles, called Milky Spoor Disease. Larvae tend to feed mostly on lawns, so thoroughly treat your lawn, and encourage neighbors to do the same.
The adults can be tricky to control, depending on the location and the population.
In a very small area you can protect the plants with row covers. Then the beetles simply cannot reach them. (you may need to hand pollinate some crops)
You can hand shake the beetles off and kill them.
You can try the 'safer' or 'organic' sprays such as soap, and see if it works.
You can surround your good plants with herbs that have a reputation for repelling the beetles.
There are some natural predators, but I do not know what their population is like in your area, or if it is possible to buy them.
Controlling the Japanese Beetle is almost a neighborhood project, since the presence of any beetles attracts more beetles. So if your neighbor only one fence away harbors them, then there will be more coming into your garden.