You can drag and drop files into OneDrive by locating and selecting them in Windows' File Explorer and moving them to the OneDrive folder.

Check out the Documents List Uploader, a sort of proof-of-concept applet from a member of the Google coding team. With it you can drag and drop files directly to your Google Docs account.

To drag and drop from a PC, simply open the Microsoft Your Phone application, navigate in the Gallery application, or manage the files and, from there, start transferring the files of your interest.