Bagworms eat the leaves of many trees and shrubs. The larvae hatch in late May or early June and immediately begin feeding. Each larva constructs a bag that covers its entire body, and to which it adds as it develops. The worm partially emerges from its bag to feed. Once all the leaves are eaten off the branch, the bagworm moves to the next branch, dragging its bag along. By late August the larva spins silken bands around a twig, attaches a bag permanently, and pupates. In the fall, the winged male moth emerges from his case, flies to a bag containing a female, mates and dies. The female bagworm spends her entire life inside her bag. After mating, she lays 500 to 1000 eggs and dies. The eggs spend the winter in the mother’s bag until next May when the cycle starts all over again.
You can spray with Sevin or Malathion which are contact sprays while the worms are feeding between late May and mid-July. Repeat after 10 days if damage is still occurring. You can also use a systemic insecticide like Orthene Systemic Insect Control or Ortho Systemic Insect Killer which is absorbed by the plant that they ingest as they feed. I use a product by Bayer called Bayer Advanced 12 Month Tree & Shrub Insect Control. It is a liquid that you mix with water and pour onto the soil at the base of the tree. I like it because you don’t have to spray.
You should handpick and destroy all the bags between now and winter to reduce the number of eggs. I would also clean up all debris below plants. You can fertilize in the spring to encourage new growth and see how the plants recover from the damage. If there is currently some green they might survive. Bagworms are more likely to kill evergreens while they may only stunt the growth on deciduous plants.