  We study anisotropies of helicity modulus, excitation spectrum, sound
velocity and angle-resolved luminescence spectrum in a two-dimensional system
of interacting excitons in a periodic potential. Analytical expressions for
anisotropic corrections to the quantities characterizing superfluidity are
obtained. We consider particularly the case of dipolar excitons in quantum
wells. For GaAs/AlGaAs heterostructures as well as MoS$_2$/hBN/MoS$_2$ and
MoSe$_2$/hBN/WSe$_2$ transition metal dichalcogenide bilayers estimates of the
magnitude of the predicted effects are given. We also present a method to
control superfluid motion and to determine the helicity modulus in generic
dipolar systems.
