Anonymous File Sharing

1. You can't use an anonymising service with P2P; peers need to know who you are.  So BitTorrent and Tor is not possible.
2. You could use BitTorrent and a 'Seedbox'; use a virtual machine at a remote location as your file sharing box, then connect to it securely (VPN, Tor, etc) in order to download the file once it has been downloaded to the seeedbox.
3. Usenet might be the way to go instead.  You can search for nzb files, and then download them from a usenet provider.  Giganews seems like a big name.  Costs money though.  The advantage of usenet is that your traffic to the usenet host is encrypted, and the files remotely reside... all over the place.