Well, I've done a bit of experimenting here too. I must first strongly caution against pigs with other animals. They like us, are omivores, and I've seen them kill and eat hens and roos and ducks alike. (and turtles and injured cats and.....) Thats a no. Little goats (like my nigerians dwarfs) are ok with geese. Probobly ok with ducks. Probobly ok with chickens. Probobly not ok with any turkeys, or if the geese are too unfriendly (like in mating time) bad news maybe. Geese can really hurt a goat.
Waterfowl should not be kept with chicens or turkeys. The reason is that waterfowl are natural carriers of AI (Avian Influenza) and they can and probobly will give it to your chickens. Now, they don't just give it too them once, they can give it to them over and over, messing up layers and killing the weak, and weakening the strong. Now, that said, if you have a few birds (a dozen geese, a dozen ducks, and a dozen chickens) in a 2 acre+ yard year round, you might be ok. If your keeping them confined in a pen smaller than that with 30 or more mixed species, you're gonna have AI problems. I learned this from our stap NPIP inspector when they tested our waterfowl and chickens a month ago. For the winter I put them togather. When we NPIP tested (I ship eggs and birds) they also AI test chickens and turkeys. Mine had it from living with waterfowl. Now, they come back 3-5 weeks later and retest. If mine still have it, I will have to seperate them permanently, and keep the waterfowl away from turkey/chicken areas. Total seperation always.
If I had known that, when I brought the free rangers in from being spread out all summer, I'd have seperated them all into two different pens for sure.