Software to act as sound card and transmit across network

Solution 1:

You may want to see if pulseaudio meets your requirements.

PulseAudio (formerly PolypAudio) is a cross-platform, networked sound server project. It is intended to be an improved drop-in replacement for the Enlightened Sound Daemon (ESD). PulseAudio runs under Microsoft Windows and POSIX-compliant systems like Linux. PulseAudio is free software released under the terms of the GNU Lesser General Public License (for the software library portion) and the GNU General Public License (for the sound server itself).

Solution 2:

you may want to have a closer look at Shoutcast, a media streaming server

and here's a Guide to setup and configure Shoutcast for LAN audio streaming