How can I install closet doors for a very long closet opening?
I would suggest that you make the doors yourself out of 3/4" birch veneer lumber core plywood. Using a conventional double track system for sliding doors you can install three doors, one on the front track and two on the back track. The front sliding door was normally kept in the center position but could be pushed left or right (you pick which choice is suitable for your application) to access the center portion of the closet. 

For sliding doors like this it is typical to have the doors overlap some so that floor guides will stay engaged with the doors. In an application like this you install two sets of floor guides and then install a stop on the front track to restrict the slide range of the center door to be left or right only.

For a 120" opening to allow for about 2" door overlap each door would be about 42" wide. This can be easily cut from a 48" x 96" sheet of the lumber core plywood. You would need three sheets total.