depends on what you want them for & what you are feeding them.
Layers pellets are potentially Fatal
to goats (I have heard of several cases of dead & very ill goats who found their way to layers pellets)
One pig is a lonely pig.
We kept our boar with the goats while his future wives matured - he ate everything he could, and did pester them as he became sexually mature. And however awkward you think a randy male is... a femal in season is worse!!
So what gender & breed (ie size) are you thinking of getting?
the poultry will be after everything elses' cereal food - so if you're wanting layers they may get fat on grain. ANd a hungry pig or goat will find a way into their housing if you feed them in there. Pigs are a million times stronger than you can imagine!
Goats will strip an apple tree of all its leaves & bark if they feel like it - they 'll need other browse too,
not grazing as much.
Pigs will eat all the eggs they find & can eat small birds (heard of some that ate a buzzard once!)
and even with nesting boxes, a broody hen will lay wherever she chooses
If you are allowing them all the whole orchard, the pig (s) will root it up, making it unpleasant for the goats.
goats also need access to shelter - they hate rain & wind, and won't thank you to fight for space with a sleepy pig, unless they can climb over them! which they will, especially goat kids playing "king of the castle!"
if you want milking goats, you'll ned somewhere well, well, well away from the others to milk - tpigs & chickens will be in the buckets as soon as look at you!
on the whole, things like worms & most diseases shouldn't pass from one to the other (except of course the chooks & turkeys) but beware that things like coccidiosis could kill any of the young ones.
hope that helps, and doesn't read too negative.