If you just want to have access to your files, you can use nfs, but you say that you already do that. If you want to do it from anywhere on the internet, not just your home network, I guess a simple solution would be to install apache and point it to your media directory (maybe also password protect it in apache).
For streaming, I have no experience myself, but I hear icecast works fine:
http://www.icecast.org/