  Using heat kernel estimates, we prove the pathwise uniqueness for strong
solutions of irregular stochastic differential equation driven by a family of
Markov process, whose generator is a non-local and non-symmetric L\'evy type
operator. Due to the extra term $1_{[0,\sigma(X_{s-},z)]}(r)$ in multiplicative
noise, we need to derive some new regularity results for the generator and use
a trick of mixing $L_1$ and $L_2$-estimates by Kurtz and Protter \cite{Ku-Po}.
