  We show the strong well-posedness of SDEs driven by general multiplicative
L\'evy noises with Sobolev diffusion and jump coefficients and integrable
drift. Moreover, we also study the strong Feller property, irreducibility as
well as the exponential ergodicity of the corresponding semigroup when the
coefficients are time-independent and singular dissipative. In particular, the
large jump is allowed in the equation. To achieve our main results, we present
a general approach for treating the SDEs with jumps and singular coefficients
so that one just needs to focus on Krylov's {\it apriori} estimates for SDEs.
