Boosynbella, do you have a compost pile?  I am leaning towards a virus/bacteria infection of some sort. But something to think about:  I had a dog, cat and chickens get sick with the watery, mucousy greenish diarrheaand actually to young cats died  and like your pets the deaths came fast.  I kept thinking they were being poisoned as well.  I wondered what could be getting all different types of animals sick.  I started to get paniced and thought about calling for help.  As I was researching to see what was going on I came across several articles about composts and how they can poison animals.  Our compost is near a hill that when it rains the run off forms a pretty good puddle.  So my animals were drinking the run off water.  We actually did away with our compost pile until we find a better location, and coincidentally  no more sick animals.  I never had my pets tested, but I believe from the symptoms and the fact they got better when the compost was remove, that was the problem. They would be fine one day then the next, extremely sick and die very shortly after. If the calf and deer deaths are not related to the chickens maybe this is a possibility.