I would be worried about the no water thing as they have been vomitting and losing liquid and water, say mineral water or purified water shouldnt do them harm................my opinion only. If they get dehydrated they will have to go on a drip and there is chance of damage to internal organs.
Linda, I know this sounds daft but if the vet is saying its not the washing up water then all 3 of them must have been at something else, maybe something that is not there now as they have eaten it. Its something that your other cats havent touched cos they either couldnt reach it or the 3 boys had eaten it already.
So what, food, sweets, alcohol, plants, something just put down and forgotten about, something someone or cat brought into the house, toy, christmas decoration or tree, something so tempting that all 3 boys had a go at it, serious brainstorming for the ridiculous needed, Where cabn the boys go that the others cant? Can they open cupboards or drawers or get into a room where they are not allowed. Check under furniture, beds, inside cupboards and drawers. look on shelves and in corners and behind things, in their bedding, somewhere they may have hidden something. What have you thrown in the dustbin or the waste in the last 24 hours.
Somewhere there must have been something that was big enough for all 3 to have a go at.
dont know if any of that helps but there must have ben something even if it is no more. One other thing is that they are being sick and do not have diarerah, to me that says poison, could be a liquid, do you have a medicine chest or tablet bottles, anything to do with car or cleaning round the house, soap.................maybe one of the vet nurses here can think of things that could cause this effect and whether the vet should be carrying out somekind of tests.
