Feed them a mixture of fruits and vegetables as well as freshly killed dead insects. If you live in other parts of the world and would like to know what to do with your live katydid, contact me and will help you to keep it alive. Don't expect your katydids to live long in captivity. Most adult katydids do not live more than 2-3 months, often less. Most are omnivorous and will accept almost any organic material as food.
Most crickets require considerable level of humidity so, spray their containers frequently.
In nature, tree crickets feed on flowers and fruits, but also aphids and other small insects. You can feed them apples and other sweet fruits as well as honey. Unlike katydids and crickets, grasshoppers are not easy to keep in captivity and most will die soon despite your best efforts to keep them alive. They require relatively low humidity and a lot of sun, which can be very difficult to provide in a small jar or terrarium. Still, some species can be kept alive for some time.