I did a similar setup a few years ago for the ps2 with a pc capture card and an external powered video splitter/distributor from radio shack, the splitter allows an input from RCA or S-Video to be output to multiple devices. So had one set of cables running to the capture card and the other to the tv
actually now i would probably replace the capture card with a usb external Adaptec Gamebridge device or something easier
for this of course you would have to use the S-Video/RCA cables for the 360
there are a bunch of vga video splitters on ebay for under 20 bucks (monoprice makes them too), dont know the quality of the signal passthrough, but you could snag one of those and then get a pc capture card/breakout that has a vga input.
either way similar concept
console > single input splitter > (output1) capture device w/vga in > pc software
console > single input splitter > (output2) tv
if you really want to get fancy you could get a dual input vga splitter and hook in the pc video card and the xbox to the inputs and the outputs to the tv/pc/capture device, then you can switch with the push of a button instead of swapping cables back and forth.
an example I found, do an ebay search for Startech 4 Port Dual Input VGA Splitter.
at a glance it looks like that Startech unit can accept 2 inputs at once and you can choose by the push of a button which outputs are synced
so with a dual-input vga, at the push of a button:
PC Video Card > (Input 1) Dual Input Splitter > (output1) pc monitor
PC Video Card > (Input 1) Dual Input Splitter > (output2) tv
Xbox > (Input 2) Dual Input Splitter > (output2) tv
Xbox > (Input 2) Dual Input Splitter > (output3) capture card w/vga in > pc software
as usual do your own DD/research on the components you wish to buy, i havent purchased or physically put together a setup with the vga solution, so i dont know how well it works 1st hand, but I hope it helps get you on the right track