Sung to the tune of "Leg bone is connected to the Thigh Bone..."
360 is connected to the VCR-input
VCR is connected to the TV AV-in
TV is connected to the Stereo
And praise the name of the Lord!
With this setup, you can also record bits of games if you want. Another way to do it is to connect the 360 directly to the TV, and the TV to the Stereo using the AV-2 of the TV or the HDMI of the TV+the digital sound cable.
But I prefer the AV inputs myself. Simpler, less likely to be hard on the wallet, or break because of some picky "priority rule" that's on page 348 of the user manual.
I've also used the TV inputs (coaxial) on occasion and don't much notice a difference between those and other analog connections. Even with my flatscreen TV. Analog simply looks worse than HDMI+digital sound, so I don't pick bones about which analog wires I use.
PS: if it's just the sound you're missing, and you're using HDMI, then get a digital sound cable and hook that up to the TV too.