Let $\Phi$ be a Young function and $\omega$ be a weight on a locally compact group $G$. For any $S\subseteq G$, a family of left translations $\{L_s\}_{s\in S}$ on the weighted Orlicz space $L^{\Phi}(G, \omega)$, is defined by $L_s f(t):= f(s^{-1}t)$ for all $t\in G$. It is said to have an \emph{$S$-dense orbit} if there exists a function $f\in L^{\Phi}(G, \omega)$, such that $Orb_S(f)=\{L_s(f): s\in S\}$ is dense in $L^{\Phi}(G, \omega)$. We show that no compact groups $G$ have an $S$-dense orbit in $L^{\Phi}(G, \omega)$. Also $S$-dense orbits may occur only on the infinite dimensional weighted Orlicz spaces $L^{\Phi}(G, \omega)$ with the second countable locally compact groups $G$. Moreover, we give a necessary and sufficient condition for $\{L_s\}_{s\in S}$ to have an $S$-dense orbit in $L^{\Phi}(G, \omega)$.
