You could also make a tincture with oregano and ACV, and add that to their water. Not sure how much to add however...the tincture has to soak for about a month to extract, and should be shaken daily. I have made tinctures, and it just sits on the counter and the time passes pretty quickly. Put at least an ounce of oregano or simply stuff oregano into a pint mason jar, cover with the good ACV, and cap tightly. Put wax paper or plastic wrap between cover and jar as the ACV will rust the lid if it is metal. When finished, strain. I would do 5-10 drops per gallon...not lots.
The tea idea is a good one as well, and that can be added to their water.
Another thread I read said 1 drop of oregano EO per gallon of water, just as a health booster. I do think 2-4 tsp might be a bit much per gallon, that oregano EO is pretty concentrated stuff. Just saying. That amount might be correct if you infused oregano in olive oil, say, which is not the same as the EO.
I put my dried crushed garden oregano in their nest boxes, along with other herbs, dry, and in their dustbox as well. They loved it in the dustbox for sure. They also ate it fresh from the garden last summer (!).
Rosemary is another herb I am looking at for its benefits.