Given this list of protocols used by the internet does anyone know any way of getting information on the amount of data (or any other usage metrics) for various ones?
The only thing you could do would be to monitor the kind of traffic flowing over your own network, and if your network is broad enough and unrestricted, then chances are what you see will be typical of a much larger dataset.
But as John commented, there's no practical way of knowing this worldwide. There's just too much data for anyone to sift through for starters, and too many sources run and owned by too many people.
For some basic protocol stats, try something like bandwidthd to get stats like this: