  We consider multidimensional SDEs with singular drift $b$ and Sobolev
diffusion coefficients $\sigma$, satisfying Krylov--R\"ockner type assumptions.
We prove several stability estimates, comparing solutions driven by different
$(b^i,\sigma^i)$, both for It\^o and Stratonovich SDEs, possibly depending on
negative Sobolev norms of the difference $b^1-b^2$. We then discuss several
applications of these results to McKean--Vlasov SDEs, criteria for strong
compactness of solutions and Wong--Zakai type theorems.
