If they were outside just before this happened they may have gotten into something toxic such as antifreeze and that could be deadly.
Usually a food change a cat finds irritating just means they throw up that one meal not continual vomiting.
Parasites can cause this but it seems odd that they all got to the same stage of infection with them at the same time.
You really do need to see a vet. Tests can be run to see if they ingested something toxic. And a vet can give them antinausea shots, fluids etc depending on what is found.
They've been being ill a long time for a small animal and probably need supportive care if nothing else.
I don't think a home remedy will solve this for you and cats being so sensitive to medicines really can't use over the counter meds without vet direction.
Hope this helps you!
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