Fungus gnats are more an annoyance than anything. Severe infestations might be detrimental to seedlings and young plants, but mainly they just eat organic matter and fungus in the soil and don't seem to affect the roots to any significant extent. They'll tend to get themselves stuck in the trichomes of the lower buds, so it is best to avoid them during flowering.
Prevention is best. Yellow sticky traps are indispensable for soil grows, use both kinds: some hang from the ceiling or other places, some come on stakes you stick right in the soil. I prefer the Safer brand with the green plastic stakes; they set up easier/cleaner (you are less likely to get sticky shit all over your hands) and seem to be more efficient/ergonomically designed.
Bti - Bacillus thuringiensis isreali is a natural bacterium that produces a larvacide which is toxic only to a handful of species of insect larvae including fungus gnats and mosquitoes. It is widely available in compressed circular pucks under the brand name Mosquito Dunks, sold in hardware stores all over.
Neem drench should kill adults, eggs, larva, etc. but I shy away from it as azadirachtins are broad spectrum fungicides and I am uncertain what it does to beneficial bacteria and fungus.
Pyrethrum is an excellent botanically derived pesticide that breaks down rapidly, it can be sprayed on soil surface to kill adults.
Gnats can easily be vacuumed. Rustle the pots a little bit to get them hovering above the soil surface and have the vacuum nozzle waiting to bring them to their sucky doom. Be sure not to snag a leaf, branch or worse in the process.
Beneficial nematodes, predatory mites and the Bti I consider to be the best for prevention and control. Those are all biological controls and are excellent for use in organics.
I would discourage the use of any 'no pest strips' in the grow room, don't know what kind of chemical vapors they put out but they can't be good.
