It depends on how long you plan on staying in the parks. Last time there, my 3 and 6 year olds took afternoon naps in the strollers and we kept going. Yes, even my 6 year old took a nap. Unheard of in the real world, but at the "World" you just never know. With the long days and nights, and hot weather, everyone gets tired.
Now if you plan on going back and doing the afternoon break thing, then no, you may be able to get away without a stroller.
AK is so crowded most days that a stroller is a good way of keeping up with the kids. And yes, the strollers are what makes it more crowded, but its a catch 22 kind of thing.
Epcot-WS, definitely a stroller. It's a lot of walking.
Play it by ear. The good think about Epcot is that if you don't get a stroller at the main entrance at rope drop, then if you need one later and your at WS-then go to the International Gateway and pick one up.
I leave in 2 days! Now my kids are 5 and 8. I'm going to play it by ear. If I'm not ready to leave and my 5 year old is tired of walking, then I'm getting a single stroller.