tl;dr: No, unless you have 200 billion nuclear bombs.
Use that to work your way up to larger and larger asteroids, until you slam Ceres into the Moon.
> "If MAD happens (ie USA/RU nuclear bombing each other), then the axis of the earth would permanently be altered and every human on the planet would not be able to survive"
I guess the modern era can look at that with some scrutiny; but 40, 50 years ago, that could've been a real fear?
We don't need to stop the moon to change its orbit. With careful and deliberate adjustments via bombing and letting Earth gravity do its job, we could alter its orbit by adding to its force vector instead of trying to negate it.
The energy required to achieve a specific Δv is the same whether you are accelerating or decelerating. This is because energy change associated with velocity (ΔE) in a conservative system is dependent on the square of the velocity change (Δv^2), regardless of direction.
What if we just wanted to slow it down 0.0000000000000000000000000000000000001% ? (which will alter it's orbit).
That seems totally doable.
But of course, the question was asking for a significantly altered orbit, which this most definitely isn't.
This would work better to change the orbit of a small asteroid. For the moon it would take (a lot) longer.