I find neem oil to be very VERY overrated.. it's never done anything for any bug problem I've ever had either on weed or on houseplants... I would get some insecticide soap (preferrably with spinosad in it) and wash them down to get rid of the neem oil and to kill off the spider mites. Spinosad will also take care of aphids, thrips and whiteflies if you're ever facing THOSE pests so it's a good thing to have on hand in any grow....
As far as fungus gnats are concerned, they're a different problem... they live IN the soil - and they like living in WET soil.. so that tells me you're watering these little ones too much. Let them dry out completely and while you're waiting for that, go out and buy some Mosquito Bits ... when the plants are completely dry and need another drink, use the Mosquito Bits to make the water (you have to soak a certain amount of them in water for 30 minutes, then strain them out and use the water that's left) ... this will kill the fungus gnats and their eggs/larvae where they live - in the soil. It works a treat, it really does!
Good luck!