I use org-mode and I have android mobile devices. I ought to try MobileOrg.
But configuration is quite rough, and these are information I found lacking:
This won't be a synchronization of files as Dropbox handles usually.
Instead you'll need to push/pull (thanks to M-x org-mobile-push or M-x org-mobile-pull) your normal off-line org-directory (which is outside of the dropbox) towards an on-line org-mobile-directory which is on the dropbox. The dropbox directory contents will be generated along with meta-information and new files (as the index.org) that allows the mobile application to find all your files.
So don't try to synchronize directly your org files by putting them in the dropbox !
Second, the MobileOrg Android app needs to know where to find the index.org file. You'll have to give the path of this file, and you'll have to start with a slash "/" for the root of the dropbox, then type the path including the index.org. For example:
If your index.org file is in the dropbox root and then the MobileOrg directory, then you must inform your mobile devices that the path is /MobileOrg/index.org. Don't forget this first slash.
But if you want to install and use that application, I won't be giving you enough information: you can read OrgMode manual on that subject, then MobileOrg Android wiki... And that was enough for me to get it running.