  For a measure space $\Omega$ we extend the theory of Orlicz spaces generated
by an even convex integrand $\varphi \colon \Omega \times X \to \left[ 0,
\infty \right]$ to the case when the range Banach space $X$ is arbitrary.
Besides settling fundamental structural properties such as completeness, we
characterize separability, reflexivity and represent the dual space. This
representation includes the cases when $X'$ has no Radon-Nikodym property or
$\varphi$ is unbounded. We apply our theory to represent convex conjugates and
Fenchel-Moreau subdifferentials of integral functionals, leading to the first
general such result on function spaces with non-separable range space. For
this, we prove a new interchange criterion between infimum and integral for
non-separable range spaces, which we consider of independent interest.
