Hello & welcome, I am Dr. B, a licensed veterinarian and I would like to help you today. I do apologize that your question was not answered before. Different experts come online at various times; I just came online, read about your situation, and wanted to help.
Based on your history and the face we have multiple goats showing signs, this raises serious concerns of a shared exposure (ie toxic plants, pesticides, heavy metal, water contamination, grain overdose etc) or possible infectious agent (ie listeria, etc). The former being especially a worry if they are on land with a range of potentially toxic plants.
In this case, we do need to tread with care. If they cannot keep anything down at all, then we may need their vet out so that injectable anti-vomiting medication can be started to break their vomiting cycle. Otherwise, if they are more settled now, you can try oral treatment for them. Now if you think they have eaten something they should not have, you can consider syringe feeding OTC activated charcoal. This can be stomach tubed or syringe fed as a slurry at a dose of 3 grams per pound of their estimated weight every 8 hrs. This will help absorb the toxins present and reduce its effects for them.
Further to this, we can combat nausea to help get them back to eating by treating with Milk of magnesia. This can be given at a dose of 15ml every 8-12 hours. And once they are more settled, we'd want to to encourage eating and drinking. Or if they are reluctant and appearing dehydrated, we can stomach tube electrolytes to maintain their hydration here. Though if severely dehydrated already, fluids (either under the skin or IV) may also be indicated. Finally, if there is any concern of infectious agents (ie if they have a fever), you can also cover bases with Penicillin from your local farm supply shop.
Please take care,