If it's holes in the leaves, for the broccoli it's the larvae of the cabbage moth, a white or pale yellow moth that's about 2" across. The caterpillars leave holes and jagged edges, and they are the same slightly blue-green color that the cabbage or broccoli is. Look on the undersides and along stems and edges. They may be as small as 1/4" or as large as 2".

For the lilies, it's the red lily beetle larvae which are brownish and carry their excrement on their back.

For both, I dump the larvae into a container of slightly soapy water to drown, and any adult lily beetles I catch (early morning when it's cool is a great time) get the same treatment. When disturbed, the adults usually drop straight down, so I hold the contain under them and just flick them in.

Sorry but no idea on the petunias.

elihja,

go over to Marvin Grain on Cove Rd and get a bottle of Captain Jacks Dead Bug Brew. that will take care of anything eating your vegetables. For the Red Lily Beetle get a bottle of Bayer Advanced Rose & Flower Insect Killer, they carry that at Home Depot or Lowes but since you'll be at Marvin Grain you can ask them about the Lily Beetle.

I am not anti-mannmade-chemical, but I do use them only after reading up on them in scientifically-based literature and I do my best to choose the least harmful alternative, which sometimes includes not growing a particular plant. Personally, I wouldn't use Bayer Advanced, and I'd advise anyone who chooses to do so to act with good info and care as to timing so that it isn't likely to be present in the plant when the flowers bloom. Its main ingredient is Imidacloprid which is a systemic insecticide that acts as an insect neurotoxin and is one of the insecticides in the general class of neonicotinoids, which have been getting a fair amount of press for the last few years. The problem is that they are nonspecific and act generally on all insects and are long-lasting (info says protection for 30 days). So if you put it on your lilies, and then bees and other pollinators visit the blooms, it will kill them, not just the targeted bad bugs. IME knocking the lily beetle larvae and adults into soapy water is more time consuming, but effective and far healthier for the garden as a whole, but others have said that Bayer Advanced is the only insecticide that seems to work on the lily beetles.

Captain Jacks Dead Bug Brew contains spinosad, which comes from a bacteria. It has similar effects on bugs that it effects to neonicotinoids in that it works as a neurotoxin, but once it has dried for 3+ hours, doesn't have nearly as much effect on bees. So it's much safer to use in the garden. I know it's effective for caterpillars of various sorts and thrips, but I don't know if it has any effect on red lily beetles.

Another option for caterpillars like the ones on the broccoli and other cabbage family plants is Bt, a bacteria that only harms caterpillars. It's most effective when used on smaller caterpillars.