  Quantum photon effects in vacuum provide an interesting setting to test
quantum electrodynamics, serving as a source for predictions about physics
beyond the Standard Model. In this paper, we investigate these effects by
calculating the one-loop Euler-Heisenberg-like effective action within a
Lorentz-violating scalar quantum electrodynamics framework. In both CPT-even
and CPT-odd scenarios, we obtain the exact result in all orders of the stress
tensor $F_{\mu\nu}$ and evaluate explicitly the lower orders of this effective
action. We identify the quantum effects coming from Lorentz violation in an
explicitly gauge invariant way. Nonlinear Lorentz-violating contributions that
may affect photon-photon scattering are explicitly evaluated.
