Other than being Linux-based, and a suggestion I read somewhere that the base distribution may be Debian there doesn’t seem to be much on the web about the operating system for the Elonex One.
Wikipedia has a small stub which states “Linos is a embedded distribution of Linux used by Aware Electronics in their A-BOOK products”. I’ve done much Googling but haven’t found a great deal more than this.
I emailed Elonex a couple of days ago asking if there was any more information available on Linos, but haven’t heard back from them yet. As ever, will keep you posted when they do.