You can accomplish what you want to do with iTunes. It all depends on how accurate your ID3 tags are, and how you are sorting the albums in the iTunes window.
Let's look at your Beatles albums. You should set the Artist and Album Artist tags correctly. For most albums these two things will be "The Beatles." For an album like the Yellow Submarine Soundtrack, though, some of the tracks are performed by the "The George Martin Orchestra." So for those tracks the Artist will be that, and the Album Artist will be "The Beatles." Setting an accurate Album Artist will also solve your complication problem.
When you have the Artist and Album Artist tags set, how should you sort them? I use the Album List in iTunes, and I almost always sort Album by Artist/Year, or Album by Artist. This groups all albums by a particular artist together, just like you want them to be.
BABBOvicenza wrote:
Also, are the files stored and organized by this application or does the application read them from somewhere else on the hardrive?
Both. In iTunes Prefs > Advanced there are two options for how iTunes will organize your files.
