Hi,
What version of iMovie and what operating system do you have on your computer?
First, you need to find out what you've got in these folders. Do a Control-Click/Get Info on them and see if they have significant data content, and what app is mentioned in the "open with" box, including those listed in the drop-down when you click on the down arrow.
Then, for each folder, do a Control-Click/Show Package Contents. What is displayed when you do that?
If these folders were created in 2011 they would be iMovie '11 (iMovie 9) folders. However, they look like iMovie 10 folders, with the exception of the iMovie Projects.localized folder. Could these movies have been done in 2013 rather than 2011? That would make them iMovie 10 folders.
Try double clicking on each folder to see what happens.
With the Theater folder, when you do a Control-click/Show Package Contents you might see a list of archived movies. If so, you can press down the Option Key and, while holding it down, drag out the movies to your desk top. They are independent movies that you should be able to play by clicking on them.
With the Library folder, if it opens in iMovie 10 (assuming that you have that version on your computer) then you probably can access your projects, play them, or share them out as independent movies. This assumes that the media for the projects are contained in the library.
The iMovie Projects.localized folder might be an iMovie 9 folder. I doubt if you will find anything playable in it.
If you aren't able to access any of your older movies after doing the above, report back with your findings.
-- Rich