[Kourosh]

How about use the physical pile of paper as part of your inbox. In other words, work through the pile as you would an inbox, i.e. if it takes 2 minutes do it, otherwise file it, delegate it, turn it into a project, or trash it. Any of these latter options could be tasks in OmniFocus. If there is a way to connect to a particular task online by URL, you could copy and paste that URL into a note field of a task in OmniFocus.

If the piles are particular large, you could do as whpalmer suggests and move through a part of the pile regularly until it is cleared.