  We study the degenerated It\^o SDE on $\mathbb R^d$ whose drift coefficient
only fulfills a mixed Osgood and Sobolev regularity. Under suitable assumptions
on the gradient of the diffusion coefficient and on the divergence of the drift
coefficient, we prove the existence and uniqueness of generalized stochastic
flows associated to such equations. We also prove the uniqueness of solutions
to the corresponding Fokker--Planck equation by using the probabilistic method.
