Cat peeing and pooping out of litter box?

If "renos" means renovation, it's quite possible that your cat has eaten some kind of building materials, maybe plaster or spackle or something, because throwing up suddenly and this change of toilet behavior is not normal. You said "I can't let them suffer" so I hope you're not considering killing a cat due to him having a problem which is likely due to the work you are doing. Perhaps keep the cats in a bedroom that is not being worked on, and put the litter box in there, until the work is done.