  We study the ionization dynamics of oriented HeH$^+$ in strong
linearly-polarized laser fields by numerically solving the time-dependent
Schr\"{o}dinger equation. The calculated photoelectron momentum distributions
for parallel orientation show a striking asymmetric structure. With a developed
model pertinent to polar molecules, we trace the electron motion in real time.
We show that this asymmetric structure arises from the interplay of the Coulomb
effect and the permanent dipole in strong laser fields. This structure can be
used to probe the degree of orientation which is important in ultrafast
experiments for polar molecules. we also check our results for other polar
molecules such as CO and BF.
