We are over run with fruit flies or small gnats. Have eliminated all sources for them to feed on and they are still present.  Do not want to use pesticides.  Humane way to catch these pesky critters

Try a mixing a cup full of apple cider vinegar with a few drops of liquid dish soap. Set it out uncovered near the place where you see the flies. They should fall into the liquid and drown.

Brent's suggestion should be effective - it may not be what the poster had meant by humane though.

If you want to live trap fruit flies google "fruit fly trap" but try replacing the usually suggested sticky liquid bait with say, a slice of rip banana. Once you have a jar full of flies you could then release somewhere else (where there is food but they will be less unwelcome). While I doubt there is any data on the survival rates for flies translocated in this way, it may ease your conscience!

I leave out the dregs of a glass of red wine, a large glass works best.  I consider this semi-humane because at least the flies go out with a big whollop of ethanol.  I also consider it easy because it means I can leave my clearing up for another day.