  We justify the feasibility of substituting a photon leg by a neutrino current
in the Euler-Heisenberg Lagrangian to obtain an effective Lagrangian for the
process $\gamma\nu\to\gamma\gamma \nu$ and its crossed reactions. We establish
the link between these processes and the four-photon scattering in both the
Standard Model and the effective theory. As an application, we compute the
processes $\gamma\nu\to\gamma\gamma\nu$ and
$\gamma\gamma\to\gamma{\nu}\bar\nu$, give their polarized cross sections, and
show how to use the $\gamma\gamma\to\gamma\gamma$ results as a check. We settle
the question about the disagreement between two computations in the literature
concerning the reaction $\gamma\gamma\to \gamma \nu\bar\nu$.
