Sorry, I saw you mentioned that after I posted...
Simple stuff like citric acid can work to knock back spider mites, or at least keep them under control, especially in veg. Or beneficial insects, they will never build up an immunity to getting eaten. If it's not a full-on infestation, the squish by hand method can also be pretty effective.
Fungus gnats are more of a nuisance than anything. Sticky traps will catch a lot of the flyers, letting the top couple inches of soil dry out will slow them down, and also "mosquito bits" from the hardware store will kill their larvae