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This paper studies the utility of the processes $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}\ensuremath{\gamma}\ensuremath{\gamma}, \ensuremath{\gamma}Z,$ and $\mathrm{ZZ}$ in searching for sources of $\mathrm{CP}$ violation arising from energy scales beyond the production thresholds of planned future colliders. In the context of an effective Lagrangian approach we consider the most general set of $\mathrm{CP}$ odd $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ operators that give rise to genuinely quartic gauge boson couplings which can be probed in $\stackrel{\ensuremath{\rightarrow}}{2}2$ scattering processes at a $\ensuremath{\gamma}\ensuremath{\gamma}$ collider. We study each process in detail, emphasizing the complementary information that is obtained by varying the initial beam polarizations. Finally, we compare our results to other constraints in the literature on $\mathrm{CP}$ odd gauge boson interactions and quartic gauge boson couplings; the search reaches obtained here are typically stronger and nicely complement previous studies which have focused primarily on W boson, top quark, or Higgs boson production.