I’m not such a big musical fan, but somehow your post struck a chord.
Here’s my own personal favorite:
[url:392fwpmd]http://www.youtube.com/watch?v=HroAq_E075Y[/url:392fwpmd]
Dude, I kid you not, I was totally listening to Stayin’ Alive by the BeeGees on repeat for the past few days so I was confused when I heard it playing in that clip you shared, OP! (I’ve also been watching that Gaki vs. Tenso dance off to this song.) XD
I also mistook musicals = stageplay, and I am aware that that is not the case all the time. Regardless, here’s a portion from a Japanese stageplay I enjoy watching, Endless Shock (2008)