You can use a Bacillus thurgensis product to deal with leaf eating caterpillars. Something like Thuricide or Dipel dust. You spray or dust it on the leaves (according to the product label) and the caterpillars have to eat it for it to be effective but it is relatively safe for aquaponics if used according to the label.
The small flying insects may be whiteflys or gnats. Yellow sticky traps can help against whiteflys and vinegar traps might work for fungus gnats. There are also some other products that may be safe to use around Aquaponics but I haven't personally used them yet so I'll let some one who has give a report on the specific products.
Diatomaceus earth which also used in swimming pool filters can be used against crawling, soft-bodied adult insects, caterpillars, snails and slugs. It is natural substance and also safe for aquaponics, sprinkle it around the base of the plants.
I would caution about using the stuff for pool filters. But you can get Diatomaceous earth that is food and feed grade that is fairly safe to use (except it is really dusty and breathing any kind of dust is bad.)
Only real drawback to DE is that when wet, it's not nearly as effective and Aquaponics tends to be a fairly wet environment.