You don't need to stream the data from the OPi, that is the wrong way for watching video because it would transcode the data on a light processor then send it unpacked on the network, which would consume a lot more bandwidth.

Once you have the files on the disk attached to the board just set up a NFS and/or SMB server on it and let the clients players mount it as a network drive and suck the data. This way you can for example have all home TV sets playing each one a different movie at the same time.