I love this conversation! I do a lot of research on holistic approaches to medicine, and Oil of Oregano is part of it.
First off, I would like to mention that you DO NOT not want to use Oregano Essential oil. Essential oil is extremely potent to a point where it can be harmful. Despite that, I've seen many blog posts for chickens taking about the benefits of essential oil.
What your looking for is Oil of Oregano. That is simply Oregano oil, and ins't nearly as potent at essential oil. They are on the right track of herbal and holistic medicine, but obviously not doing enough research.
Oil of Oregano can actually be used as a natural antibiotic in cases. I swear by it. Every time I'm exposed to a virus, I take Oil of Oregano right after, and have never caught it. This article explain more about it being a natural antibiotic. I actually mentions that it is used in the chicken feed industry for Organic Farmers who can't feed antibiotics to their birds. The article is for dogs, but its a source I trust with good info. All the benefits it talks about is the same, expect for dosage.
https://www.dogsnaturallymagazine.com/oil-of-oregano-natural-antibiotic-for-dogs-2/
Just from taking it myself, I've learned that it is very very "spicy", and actually can be hard on the gut. Its a hot oil, and its not something I would ever want to feed any animal on an empty stomach. I took it before breakfast once, and that was not fun at all. Some people can't even tolerate the oil. It has a lot of benefits, but is one of the harsher holistic remedies out there. With that said, I would not put it in your chickens water like you mentioned. I think they would be getting a lot of it, possibly on an empty stomach, and over time that could actually cause more harm than good. The only other caution I would take, is make sure you are getting Oil of Oregano. You actually have to type Oil of Oregano into the search bar, or else you will get essential oil, which is not what your looking for.
If you are looking to use oregano as an immune booster, I would simply add the fresh herb to their feed. I soak my feed, so that makes it easier, but you could mix it into their dry feed as well. I would expect a fresh herb to be more beneficial than a dried herb. Unless its freeze dried, the drying process often pulls a lot of key nutrients out of the product. I'm not sure if it would affect its ability to boost the immune system, but it might.
Yes! For myself I have. As a preventative to getting nay kind of virus, and as a general immune booster. I think that its a great preventative for all kinds of things in all animals. Though if you wanted to feed the oil on a regular basis, I would put one drop per bird in a days worth of soaked feed, maybe even less, and mix it in really well. I say that since the dosage for dogs is 2-3 drops, so 1 drop for a chicken sounds about right. Then feed that. Or if you wanted to use it as a natural antibiotic. That way they wont get it on an empty stomach, and it shouldn't be to much for them. Possibly even divide the feed between multiple stations, so all the birds get it.
Personally, I wouldn't feed the oil daily. I feel like its very strong, and could possible be pretty rough on their guts. I would stick to the fresh herb, and the oil every now and then. There are other herbs that work amazing as immune boosters and disease preventative. Echinacea supposedly will keep dogs from ever getting any viruses if you feed it before exposure, or right after. Its also not nearly as hard on the gut, so possible a good alternative. Here is an article on it for dogs.
https://www.dogsnaturallymagazine.com/can-echinacea-boost-your-dogs-immune-system/
Since echinacea isn't so hard on the gut, I wouldn't be as concerned about an exact dosage. For most herbal remedies, I don't think you can over do it, Oil of Oregano is just one that I am cautious with.