It would be my uneducated guess to say just keep eating like normal. Though, if it were me, I'd be eating less or lighter during my usual sleeping hours.
The body is going to burn a set amount of calories just to exist, and thats assuming your body gets some good downtime (aka sleep/rest). So 16 hours awake and 8 hours of sleep will burn XX amount of calories. I would assume that since you're delaying that rest, and staying awake for 20-24 hours, and then 8 hours of sleep, your body will burn more calories than a regular day.
Lets assume that you're up for 16 hours, and sleeping for 8 hours in a given day. Now for sake of the numbers, lets say each hour = 1 unit of calories. When you're awake, your body burns 1 full unit. When you sleep, your body burns 1/2 a unit. So for 16 up, 8 down, your body would burn 20 units of calories.
Now lets say you're up for 24 hours, no sleep. Your body still burns 1 unit of calories per hour of awake time, and 1/2 unit per hour of sleep time. So being up for 24 hours would burn 24 units of calories.
So aside from throwing your internal schedule out of whack, working extended hours would require additional calories.
Personally, after reading what I've read, I wouldn't be replacing meals with a milk/protein shake. I'd try to balance whatever I ate after my normal meals. Not too heavy on protein, carbs, or fats. Maybe just a meal replacement shake if you're pressed for time, but I wouldn't try to overload on the protein if you're already getting enough in your regular diet.
Also, as for sleeping 10-12 hours after being up fro 24...above all, listen to your body. If your body needs 10-12 hours of sleep to recouperate from the 24 hour shift, and it won't affect your other duties adversely by doing so, then by all means, I say do it. As far as I know, the only person hurt from sleeping too much was Johnny Appleseed.
Again, just my uneducated opinions above. I hope they help at least a bit.