  We establish pointwise estimates expressed in terms of a nonlinear potential
of a generalized Wolff type for $A$-superharmonic functions with nonlinear
operator $A:\Omega\times\mathbb{R}^n\to\mathbb{R}^n$ having measurable
dependence on the spacial variable and Orlicz growth with respect to the last
variable. The result is sharp as the same potential controls bounds from above
and from below. Applying it we provide a bunch of precise regularity results
including continuity and H\"older continuity for solutions to problems
involving measures that satisfies conditions expressed in the natural scales.
Finally, we give a variant of Hedberg--Wolff theorem on characterization of the
dual of the Orlicz space.
