  In this paper we investigate the existence of solution for the following
nonlocal problem with anisotropic Stein-Weiss convolution term $$
  -\Delta_{\Phi}
u+V(x)\phi(|u|)u=\dfrac{1}{|x|^\alpha}\left(\int_{\mathbb{R}^{N}}
\dfrac{K(y)F(u(y))}{|x-y|^{\lambda}|y|^\alpha}dy\right)K(x)f(u(x)),\;\;x\in
\mathbb{R}^{N} $$
  where $\alpha\geq 0$, $ N \geq 2$, $\lambda>0$ is a positive parameter,
$V,K\in {C}(\mathbb R^N,[0,\infty))$ are nonnegative functions that may vanish
at infinity, the function $f\in C (\mathbb{R}, \mathbb R)$ is quasicritical and
$F(t)=\int_{0}^{t}f(s)ds$. To establish our existence and regularity results,
we use the Hardy-type inequalities for Orlicz-Sobolev Space and the Stein-weiss
inequality together with a variational technique based on the mountain pass
theorem for a functional that is not necessarily in $C^1$. Furthermore, we also
prove the existence of a ground state solution by the method of Nehari manifold
in the case where the strict monotonicity condition on $f$ is not required.
  This work incorporates the case where the $N$-function $\tilde{\Phi }$ does
not verify the $\Delta_{2}$-condition.
