The calf is probably scouring because he had two quarts at once. That is too much for a newborn, and too much for a stressed and cold calf. Overfeeding is, in my opinion, the number one killer of orphan calves. If you are ever in doubt, remember it's better to have a calf that is a little bit hungry that it is to have a dead calf. Always feed weak stuff in small portions at first, and build up to larger amounts of the strong stuff.
Cut his milk out for 24 hours, give him only electrolytes in his bottle so he doesnt dehydrate and let his gut settle down. I know with holding food on such a little guy will be hard, but he will quickly dehydrate if you dont with-hold the milk. You wouldnt want to eat when you have the runs and an upset tummy, so dont try to force him. Just keep him hydrated for now.
After 24 hours, give him 1 quart of half strength milk or replacer, do this for 24 hours.
Then give 1 quart of slightly strong milk or replacer for 24 hours.
Then give 1 quart of full strength milk or replacer for 24 hours.
Then give 1 1/2 quart of full strength milk or replacer for 48 hours.
Then give 2 quarts of full strength milk or replacer.
When I say "give 1 quart or 1 1/2 quart", I mean that much EACH feeding. Make sure that his belly is empty when you feed him again.....go at least 6 hours between bottles.
It's too late to worry about colostrum. You should get some bovine electrolytes, or some clear gator-aide for the electrolyte substitute. It's very important to with hold that milk for the full 24 hours, so his digestive tract can completely empty and rest.
Get some yogurt or probios (at the feed store). If you use yogurt, get a brand that advertises for "digestive health", and add 1/2 of a small cup to EACH bottle for at least a week (any flavor).
And I would have that cow on the trailor and to a slaughterhouse, post-haste!
Poor little guy! Take your time in re-introducing food, dont rush it. He/She can still pull thru this and with a little TLC may turn out just fine.

I feel for ya......I hate having a weak little one.