How do I transfer files directly to and from Google Docs and SharePoint?
The kind of this you are asking for actually requires legal contacts between the two Companies involved. What you are speaking about is clearly not possible at all - in the same way as there is no way to transfer any of your stuff from Google+ to Facebook or vice-versa.
There may be some scripts, browser-extensions to do this or may be you can create one.
Well, I am completely sure that transferring files from SharePoint to Google Docs is not possible at all, but Transfering from Google Docs to SharePoint (or any other service similar to SharePoint) would be possible if the service has the option of Remote Upload via extrenal URL; in which case you can set your Google Docs Documents Sharing options to Anyone with the link can View/Edit and then give the URL generated to SharePoint (or any other service similar to SharePoint).
I am not sure whether SharePoint has the Remote Upload Facility or not; but this facility is do available in few Free Cloud Storage and similar categories of Websites; but again many of these websites have been recently shut down due to a new Law passed by the US Government.