Fungus gnats, drain flies, and fruit flies are not the same thing and do not share environments. So it would be good to know which one has, and their source, before treating plants that may or may not be involved. Fungus gnats require moist brown material, fruit flies require rotting greens, drain flies breed in water.
I've read many testimonials about Neem oil damaging some plants.
Bananas and tomatoes should never be refrigerated.
Dish soap is not made for plants and has substances in it that are not necessary for insecticidal purposes and could be harmful to some plants. If using this kind of method, please use insecticidal soap made for such purpose. For some reason this old wives' tale will not die, but may have been invented when there was no separate insecticidal soap vs. dish soap.
It would be a shame to damage or kill plants in the name of trying to make them better!