I have never heard of "Nyuujuu". Could it be "nyuugyuu"? A nyuugyuu is a milk cow. Are you sure you spelled that right? As for the others,
"miruku" is usually used for baby's formula (or cow's milk when used in coffe, tea and desserts), "gyuunyuu" is cow's milk and "chichi" mother's milk (human's as well as animals') in general as well as somewhat vulgar way of referring to female breasts.
I've never heard of it myself, either, even though it is found in a dictionary (大辞林）.
There seem to be three different pronunciation for 乳汁, chishiru, chichishiru and nyuujuu.
My answer to the OP is that nyuujuu is not a common word so stick to gyuunyuu and miruku and (o)chichi.