If your receiver can transcode from one video format to another (composite or s-video to component OR composite, s-video, component to HDMI) then it won't matter what video format you use from each device. That doesn't seem to be your case, so...
You must use the least common denominator; ie the highest format that all devices you want to switch can use. For HD signals (720p, 1080i) you must use component or HDMI.