Disney's Wide World of Sports hosts the Atlanta Braves spring training (e.g. pre-season) every year in February and March, so if you're going then, there's a good chance you'll see a lot of different Major League teams.
Other than that, there are a number of A-League (essentially the fourth tier of baseball) teams in the Florida State League who play not too far from Orlando - the
Daytona Cubs, the
Brevard County Manatees and the
Lakeland Flying Tigers.
And if you don't mind travelling to Tampa but don't want to see the Rays (note - they're not called the Devil Rays anymore), they also have an A-League team based there called the
Tampa Yankees.