  We consider both massive Euler-Heisenberg-like and Euler-Heisenberg-like
Electrodynamics in the approximation of the strong-field limit. Our analysis
shows that massive Euler-Heisenberg-type Electrodynamics displays the vacuum
birefringence phenomenon. Afterwards, we calculate the lowest-order
modifications to the interaction energy for both classes of Electrodynamics,
within the framework of the gauge-invariant path-dependent variables formalism.
Interestingly enough, for massive Euler-Heisenbeg-like electrodynamics
(Whichmann-Kroll) we obtain a new long-range ($1/r^3$- type) correction, apart
from a long-range ($1/r^5$- type) correction to the Coulomb potential. However,
Euler-Heisenberg-like Electrodynamics in the approximation of the strong-field
limit (to the leading logarithmic order), display a long-range ($1/r^5$- type)
correction to the Coulomb potential. Again, for their non-commutative versions,
the interaction energy is ultraviolet finite.
