  By using the It\^{o}-Tanaka trick, we prove the unique strong solvability as
well as the gradient estimates for stochastic differential equations with
irregular drifts in low regularity Lebesgue-H\"{o}lder space $L^q(0,T;{\mathcal
C}_b^\alpha({\mathbb R}^d))$ with $\alpha\in(0,1)$ and $q\in (2/(1+\alpha),2$).
As applications, we show the unique weak and strong solvability for stochastic
transport equations driven by the low regularity drift with $q\in
(4/(2+\alpha),2$) as well as the local Lipschitz estimate for stochastic strong
solutions.
