I don't think a feature such as Picture In Picture exists currently with multiple inputs as you have suggested. (though it would be very cool if it did)
You can plug in more than one video source into your monitor however you can only view one of those items at any given time, you would have to change input sources.
For example I have a Westinghouse w22v2 that has 4 different inputs:
Component which my Xbox is plugged into
Composite which a VCR or my old GameCube could be plugged into
VGA for computer A
DVI for computer B or A which I could run in either Extended, Clone or Single Large Display (Eyefinity) (the last 2 being somewhat pointless)