Soil is definitely a possibly for how you got them. If you've gotten any new plants recently, they could've been hiding on those and spread to rest.
The neem oil should have instructions on it to indicate if it's a concentrate you should dilute or ready to use. Fwiw, the concentrate is more economical and the link is what I've used.
Once you figure out the proper dilution, spray and wipe them down with it and be sure to get the underside of the leaves, they like to hide there. If it's a really bad infestation or some plants like the Peace Lily have a ton of leaves, I'd fill up a 5 gallon bucket with the neem oil solution (you'd use roughly a 1/3 of the bottle of concentrate I linked above) and dunk the plants in that upside down and swirl them around in it.
Microwaving your soil sounds like a royal pain in the ass. I'd get new soil and repot the ones you know are infected. You can preemptively spray and wipe the others and just keep an eye on them. I've managed to get rid of spider mites on plants that I've caught early without having to repot.
Mealy bugs, Neem Oil will be your biggest help Neem Oil Fungicide Miticide Insecticide Concentrate 16 fl. oz. https://www.amazon.com/dp/B00C4TSEUI/ref=cm_sw_r_cp_api_glt_fabc_C7HNRGCG0Z8S4FH9YK36?_encoding=UTF8&psc=1 I use this one, it’s super concentrated so mix with water and spray entire plant everyday.