Drupal multiple node url aliases
When you create a node they will always use the url node/[nid].

You can use the path auto module to create an url alias for the standard node. Path auto uses the token module to create the url alias for the nodes.

What you can do, is to create a token for the value of the field, and then setup path auto to use the contents of the field when creating the url alias.

Another thing you could do is to use the ShURLy module, to actual create short urls. You could make a custom module where you created or update the short url for the node when saved, and let ShURLy handle the redirects.