  In this paper,we consider the solutions of the non-homogeneous elliptic
obstacle problems with Orlicz growth involving measure data. We first establish
the pointwise estimates of the approximable solutions to these problems via
fractional maximal operators. As a result, we obtain pointwise and oscillation
estimates for the gradients of solutions by the non-linear Wolff potentials,
and these yield results on $C^{1,\alpha}$-regularity of solutions.
