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In this paper we investigate the existence of solution for the followingnonlocal 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 vanishat 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-weissinequality together with a variational technique based on the mountain passtheorem for a functional that is not necessarily in $C^1$. Furthermore, we alsoprove the existence of a ground state solution by the method of Nehari manifoldin the case where the strict monotonicity condition on $f$ is not required.  This work incorporates the case where the $N$-function $\tilde{\Phi }$ doesnot verify the $\Delta_{2}$-condition.

A Generalized Choquard equation with weighted anisotropic Stein-Weiss potential on nonreflexive Orlicz-Sobolev Spaces