Ellen,
The Disney web site has a helpful
FAQ page which lists, toward the end, all of the items that cannot be brought into the parks. It includes "strollers larger than 36" by 52" as being prohibited. If your stroller is within these size limits, you will definitely be fine.
I have never personally seen a Cast Member measuring a stroller to make sure it fits within any specific measurements. I think if the stroller isn't unusually wide or long, then you shouldn't have any problems. Disney puts these limits in place simply to protect the safety of all guests - since a very wide or long stroller would likely be bumping into and/or tripping other people, as well as blocking too much of the walking path.
For transportation, the only thing I would be concerned about is how is easy it is to fold up. You should be ready, willing and able to fold it up several times during the day for bus, train, boat, and/or tram rides.
Hope that helps.