Learn the life cycle of the insects involved...so you can use softer/harder products when you need then. If you have a county/state extension service, see if they can help you learn about the pests.

What is your soil like?
When did you start gardening organically?
Many people think that if they stop using synthetic fertilizers and broad spectrum poisons but do not work on getting their soil into a good, healthy condition they will suddenly see a decrease in insect pests, but it does not work that way. It takes time for soils that have been abused to recover, 3 to 5 years, if sufficient quantities of orgnaic matter are even added to that soil. During the transition period you may even see greater insect pest problems.
Floating row covers have been shown to help, this is disputed by people that have never used them, placing a reflective material under the plants has also been shown to help control the squash bugs, but the best way is to get your soil into that good, healthy condition so the plants growing in that soil are strong and healthy and less attractive to insect pests.

Thanks for the suggestions. I really enjoy getting advice from other gardeners! We just built and moved to small town Indiana, and are making our first full-sun garden. (Quite a change from our former full-shade, woodsy garden.) Our soil is hard clay, which was used to make the bricks of some of the historical buildings nearby. We are slowly building better soil with compost and even builders sand, and can see a difference after one year's gardening.

I'll try the floating row covers and see what happens.