Lauren,
Thanks for your question!
So I can tell you from personal experiences that yes, you can take strollers onto the
Disney Skyliner, the
Monorail, and most of the
boats. A few of the smaller boats on smaller routes might ask you to collapse a stroller, but those are pretty few and far between.
On the Skyliner strollers are fine as long as they are not larger than 30" x 48", otherwise they may ask you to collapse those as well.
When we traveled with our girls at an age where they were both in a stroller, we found it very useful to bring our own rather than just rent within the parks. It was great when we headed home from the parks at the end of the evening, since they were sleepy by then. They could doze off without having to be lugged around, and it let to easier bedtimes.
If you write me back with where you are staying, I can give you some more details on what boat lines are likely OK to keep the strollers open, and which might require you to collapse the stroller for travel.
Have a Magical Vacation!Doug