  We discover an intrinsic dipole Hall effect in a variety of magnetic
insulating states at integer fillings of twisted MoTe$_2$ moir\'e superlattice,
including topologically trivial and nontrivial ferro-, antiferro-, and
ferri-magnetic configurations. The dipole Hall current, in linear response to
in-plane electric field, generates an in-plane orbital magnetization
$M_{\parallel}$ along the field, through which an AC field can drive
magnetization oscillation up to THz range. Upon the continuous topological
phase transitions from trivial to quantum anomalous Hall states in both
ferromagnetic and antiferromagnetic configurations, the dipole Hall current and
$M_{\parallel}$ have an abrupt sign change, enabling contact free detection of
the transitions through the magnetic stray field. In configurations where the
linear response is forbidden by symmetry, the dipole Hall current and
$M_{\parallel}$ appear as a crossed nonlinear response to both in-plane and
out-of-plane electric fields. These magnetoelectric phenomena showcase novel
functionalities of insulators from the interplay between magnetism, topology
and electrical polarization.
