not sure if it can do all 4 at once, but vlc (
www.videolan.org) can record audio and video from input sources and as long as each input is configured as a separate device or has some unique way of identifying them then vlc can be scripted to rotate among the devices every few seconds, and perhaps it can read them all at once by using multiple instances of vlc but i've never tried
vlc can also be set to stream video remotely