I don't know if mudjacking would work on a concrete block wall.
Mudjacking is where they pump some kinda slurry under a solid slab to
level it once again. It works because they pump the slurry in under
pressure, and that pressure acts on the entire area of the underside of
the slab. So, even if you have a 10 foot by 10 foot slab of concrete
weighing 100 pounds per square foot, a slurry pressure of 100/144 or
less than 1 psi acting on the underside of that slab will lift it.
While some of the slurry will undoubtedly spill out from under the slab
all around the perimeter of the slab, as long as you can compensate for
that by pumping enough slurry under the slab to maintain that 1 psi
pressure, you can lift the slab.
But, pumping a slurry under a concrete block wall is an entirely
different situation. The slurry is going to rise into the cavities of
the block wall and fill up the block wall with slurry before it lifts
the wall. There may be a way to do it, but I'd talk to some of the
mudjacking companies before I assumed this could be done with
mudjacking. Even if the blocks were solid, I'd still think that
mudjacking a concrete wall would be far more difficult than mudjacking a
concrete slab just because of the leakage rates and pressure
requirements in each case.
What Philo said, and I would also use some good construction adhesive to fi
ll in the cracks in the wall as you are jacking it up, let it cure for at l
east a day before starting to push in the new footing-type concrete. The c
onstruction adhesive will help hold the wall together against futue crackin
g due to settling. That stuff is amazing.