I dont think it is advisable to use Dropbox to synch Outllook .PST files (which is where the Tasks are stored along with messages, calenders etc) due to potential data corruption / file open conflicts. See:-
http://www.msoutlook.info/question/697
and
http://lifehacker.com/5805828/how-to-sync-your-desktop-email-client-outlook-or-thunderbird-across-multiple-computers
I could be wrong, but the 'file in use:' message that you are getting from Dropbox is probably because the Outlook Application running on the PC 'Owns' the .PST/Task data file and the Dropbox service also running on the PC, is attempting to open the same data file to upload it to the Drop Servers. I dont think Outlook will allow that, as it will be seen as a Sharing violation.
You could try closing Outlook, then when Dropbox commences its synch cycle start Outlook, which might work. But even then, there is still the potential for data corruption to occur at some point. The same issue will occur when Dropbox attempts to synch data from its servers back to your PC.
As a test, when you close Outlook I think you may see Dropbox successfully copy the data file to its external Servers.
I dont have your type of Dropbox setup to be 100% certain, so apologies if incorrect.