Let \(\Phi:\mathbb{R}\to [0,\infty)\) be a Young function such that \(\Phi\) is even, convex on \(\mathbb{R}\) and \(\Phi(0)=0\). Let \(\Omega\subset\mathbb{R}^n\) have finite Lebesgue measure and \(w\) be a weight on \(\Omega\), i.e., \(w\) is a positive locally integrable real function defined on \(\Omega\). The Orlicz (resp., weighted Orlicz) space \(L_\Phi(w)\) is induced by the modular \[ \rho(f) = \int_\Omega \Phi(f(x))\, dx \quad (\text{resp.,} \quad \rho(f,w) = \int_\Omega \Phi(f(x)) w(x)\, dx), \] and equipped with either the Luxemburg or Orlicz norm, which are equivalent. The definition can be formally generalized by replacing the Lebesgue measure by a general \(\sigma\)-finite measure space \((\Omega, \nu)\), where \(\Omega\) is an abstract set. Below there are samples of the main results which also hold true for general non-atomic \(\sigma\)-finite measure spaces. Theorem 1. Let \(\Phi\) be a Young function and for \(K>0\) put \(L_K(t) = \Phi(K\Phi^{-1}(t))\). Let \(S_K\) be the complementary function to \(L_K\) and assume that \(w\) is a weight function, bounded away from zero. Then \(L_\Phi(\chi_\Omega) = L_\Phi (w)\) if and only if there exists \(K>1\) such that \[ \int_\Omega S_K(w(x))\,dx 1\). Then \(L_\Phi(w_1) \hookrightarrow L_\Phi(w_2)\) if and only if \[ \int_\Omega S_k(w_2(x)/w_1(x)) w_1(x)\, dx 1\). The applications of the above theorems allow to provide criteria for a composition operator to be continuous on \(L_\Phi(\Omega)\). This is an improvement and simplification of results in the literature. The main theorems are proved by using the techniques developed in the theory of Musiełak--Orlicz spaces.