As you mentioned it's really difficult to determine stocking densities because land productivity is so variable in the northeast. You'll also find that summer drought will have you looking for more pasture some years. 20 goats/sheep don't require too much room and I think your 7 acres would be a good target. Although, you'll also want to consider if there's an area you'd like to stockpile for fall grazing.
I'd imagine you'll graze your poultry after your sheep/goats so I'm guessing that won't take additional land. However, pigs are always a challenge if you're grazing them. If you're trying to raise pigs in a silvopasture and without destroying your soil and trees you'll need a lot of space and the ability to move them every couple of days. Watering can be a challenge for pigs on pasture. I don't have a good recommendation for you on amount of land for your pigs but I would say at least a couple of acres with sound electric fence and many paddocks (like 20 or more).
The other thing to consider is if you're looking at silvopastures (which may be less productive) or open pastures for your grazing. If you're using silvopastures the variability of forage production could be half (or less) that of open pasture if your tree density is high.