Seeking one interface for all my ebooks

I’ve begun to acquire mostly ebooks instead of printed books, and I’m frustrated by the way ebooks are associated with a particular software program. I usually read them on a portable device (iPod Touch, Kindle).

For example, my Kindle books are not visible anywhere but the Kindle reader. My Nook books are not visible anywhere but in the Nook reader, etc. Even PDFs become associated with the program I use to load them onto my device.

So, not only do I have to recall that I have a particular book, I have to remember which program it is associated with. This is one of my new aggravations. It’s like if I purchased a book from Barnes and Noble and need a special pair of Barnes and Noble glasses to not only read the book, to even see that the book exists.

I want things to work like on my PC. I can load all my books, or music, or whatever into a common location, and then view/listen to them with any program I choose.

Has anyone found a way to accomplish this on portable devices (IOS or Android)?
I’m have the Calibre program on my PC, and I suspect there may be a way to use it as part of a solution. Any advice or suggestions welcome.