  "Einstein-aether" theory is a generally covariant theory of gravity
containing a dynamical preferred frame. This article continues an examination
of effects on the motion of binary pulsar systems in this theory, by
incorporating effects due to strong fields in the vicinity of neutron star
pulsars. These effects are included through an effective approach, by treating
the compact bodies as point particles with nonstandard, velocity dependent
interactions parametrized by dimensionless "sensitivities". Effective
post-Newtonian equations of motion for the bodies and the radiation damping
rate are determined. More work is needed to calculate values of the
sensitivities for a given fluid source, so precise constraints on the theory's
coupling constants cannot yet be stated. It is shown, however, that strong
field effects will be negligible given current observational uncertainties if
the dimensionless couplings are less than roughly 0.01 and two conditions that
match the PPN parameters to those of pure general relativity are imposed. In
this case, weak field results suffice and imply one further condition on the
couplings. Thus, there exists a one-parameter family of Einstein-aether
theories with "small-enough" couplings that passes all current observational
tests. No conclusion can yet be reached for large couplings.
