L.R.
He may have a ton of mucus still hanging aroudn fro the colds etc. Often kids (and adults) have mucus that doesn't "show up" as a stuffy or runny nose but is still in the nasal passages, back of the throat, etc. That could be part of the problem. The mucus may mean that when he then runs and bends, what's coming up isn't the milk or food really but more mucus.
The running around followed immediately by a sudden movement like bendig over or squatting sounds like an issue too. He might be the kind who just should not drink or eat when hes' going to move around immediately afterward.
Third thing to consider-- acid reflux or maybe allergies. Is it always and only milk that this happens with? If so -- try taking him off it for a while and see what happens. He may have issues digesting it.