  We study the bulk and finite-size critical behavior of the O$(n)$ symmetric
$\phi^4$ theory with spatially anisotropic interactions of non-cubic symmetry
in $d<4$ dimensions. In such systems of a given $(d,n)$ universality class,
two-scale factor universality is absent in bulk correlation functions, and
finite-size scaling functions including the Privman-Fisher scaling form of the
free energy, the Binder cumulant ratio and the Casimir amplitude are shown to
be nonuniversal. In particular it is shown that, for anisotropic confined
systems, isotropy cannot be restored by an anisotropic scale transformation.
