I guess WLAN is not the best possible for this, but my home WLAN speed is 54Mb (~ half from normal 100Mb LAN speed, 5-6Mbytes per second), so I guess it should be easily enough for decent quality. For example when comparing to XviD quality that has normally 1000-2000kbit for video and 192-500kbit for AC3 audio. Maybe I'm not counting right, but seems like there is plenty of bandwith for this kind of implementation.
PC hardware is not a problem either. PC that i'm going to use has 3GHz P4 CPU and fast DDR 400MHz memory with ATA/133 RAID with striping. Not sure what you meaned with needed equipment for AC3 encoding, but what I have is a card with optical input which I guess should be enough with some software encoder.
But the problem isn't really in the bandwith nor in hardware. It's just that I want to use stream, not some recorded video clip. What I understood was that I should put my PC to record the ongoing TV feed into some folder and configure that into RelaX + Xbox, but I don't want to record or save anything. I want to take the picture + audio and just simply stream it into my Xbox without having the stuff on my local disk. Normally streaming means connecting into some specific port which then provides the feed, just like XBMP does with RelaX. So I guess what I'm really looking here is a software or multiple softwares that together that can stream input from my video and audio devices with decent quality into format that Xbox can understand somehow and this all should happen in real time and using on-the-fly encoding.