The sticky traps aren't going to do much to keep the gnats down. They will help some, if you use enough of them, by taking adults out of circulation before they lay their eggs. But to eliminate them, you need to use a product like Gnatrol. You can get it on EBay for like 50 bucks a pound, and a pound will last you until hell freezes over. Years, most likely.
I get those bastards every single time I bust open a new block of coco. In between new coco, I can go a year or two without ever seeing one, so yeah - you can get rid of them with the Gnatrol. Gnatrol uses the same ingredient as mosquito dunks, and kill gnats the same way it kills mosquitoes - by killing the larvae before they mature and emerge from the soil. Both products use a bacteria called bacillus thuringiensis israelis, which you may commonly see abbreviated as "bti." Because that's a lot easier to type than bacillus thuringiensis israelis.
Since bti is only effective during the larval stage, you have to make sure that no larva has time to get to the pupal stage without meeting up with the bti. The larval stage can take anywhere from 5 to 12 days depending on temperature (the warmer it is, the faster they develop), so I never go more than 4 days without a full treatment. It's really simple; all you do is mix in some of the powder into the water, and feed the plants like you ordinarily would. Make sure the entire pos is soaked, and again - do it every 4 days, without fail. Skip even one treatment, and you're starting all over.
It's best to make sure you use unchlorinated water, and NO PEROXIDE in the bti mix. If you can't get unchlorinated water, it should still work, but not as well - because the whole point of chlorine and chloramine is to kill bacteria, so... yeah. Best to not use water that has chlorine or chloramine. Chloramine especially is pretty nasty stuff for friendly microbes; it's chlorine bonded with ammonia. Yuch, says bacteria.
You can call your city water department to see if they use chloramine. Tell them you have an aquarium, and the fish seem sick. If they say your city uses it, then you can remove it with either a reverse osmosis (RO) filter or a high-quality carbon water filter. If you don't have either of those, you can buy a couple of 5-gallon jugs of RO spring water at the grocery store to start your treatments. If you don't have chlorimane in your water, that's easy - you can get rid of chlorine by filling 5-gallon buckets and putting an airstone and airpump in the water. Should eliminate the chlorine within a couple of days, and you can never have too much oxygen in your water, say your plant's roots.
So. Soak your entire growing medium every 4 days, and you should be able to regain control of your room. Don't get discouraged - it can take 2 or 3 weeks, sometimes more. The adults that are hatching today can live as long as 2 weeks or more, and no matter how thorough you are, you'll always miss a few of the larvae. So even if you do it perfectly, some will survive the first couple of treatments, but you will get them all over time. Even if it takes a month or more, you will win in the end if you stay disciplined. And even after the first treatment, you're already cutting way back on the number of active larvae, which are the ones doing the damage. So you make a big difference in plant health right from the start.
If you're not using an enzyme product like Hygrozyme, you should. That helps eliminate dead organic material, like dead roots and such, that the larvae feed on.
So, once you've done all that, the next thing you need to do is quarantine everything in your room that has been, or can be, infected. Every single bit of open soil or coco probably has eggs in it, so seal them off immediately. Tightly, air tight. Then either treat those packages of soil with bti, or bake them in the oven. You can just crumble up some mosquito dunks and mix them with the medium before sealing it off, but I like to bake it just to be sure. I go 225 degrees for at least 3 hours, then let cool and package it immediately in sealed bags. You want to hit a temperature at the center of the container of 180 degrees, and leave it at that temperature for an hour or more. And that takes a while, because coco is a great insulator. I always put crumbled mosquito dunks in the packages after I bake them, but never before - because it kills the bacteria.
So, that's it. I know it sounds like a lot, but it really isn't that bad, because if you do it right you only have to do all this one time. So good luck. The bad news is, you're in for a war, but the good news is it's a short war if you really go all shock and awe on the little bastards. The trick is to get all over the fuckers the minute you see them, because if you let them run wild for a couple of weeks, the coco will just be crawling with the larvae. And since a small percentage will usually live through all but the final couple of treatments, it will take forever to whittle them down if they get out of control.