>How nutritious is milk?
Some.
>Could you live on milk and milk alone?
No you would asphyxiate.
>If so, how much would you have to drink?
See above.
>What would the effect on your body be, good or bad?
That depends on your point of view.
>Could you negate the negative ones with supplements of some kind?
Yes, supplement your all-milk diet with a healthy balanced one and you'll be fine.
Infamously David Bowie lived off peppers and milk and cocaine for a time in the seventies, but I don't know how much of this is myth-making and Chinese whispers. According to a biographer he also spent much of this time in a "state of psychic terror", though I suspect this had little to do with the milk.
A lot of weird thought experiments popping up on /nom/ and /fat/, lately.
It would help to define the parameters a bit better, because you could feasibly "live" with nutrient deficiencies for a very long time, depending on the nature of the deficiency, even if it did cause you to feel unwell.
So what, really, is your goal? What are you looking to optimise? Getting your minimum daily requirements of micronutrients and calories as cheaply as possible? With as few ingredients or as little cooking as possible? Or is your goal simply survival, or avoiding poor health?