Safe and reliable operations of lithium-ion batteries in electric vehicles (EVs), etc., highly depend on the accurate state of charge (SOC) estimated by the battery management system (BMS). However, due to the battery's nonlinear operating conditions and complex electrochemistry, accurately estimating SOC is a major challenge. In this paper, an adaptive strong tracking square-root extended Kalman filter (ASTSEKF) with nonlinear condition adaptability is proposed for the recursive correction, denoising, and op4timization of the SOC estimation of lithium-ion batteries. The proposed ASTSEKF optimizer introduces an adaptive fading factor, a weight adjustor, and a strong tracking filter to recursively update the posteriori error covariance matrix using a Cholesky decomposition and corrects the uncertainties of the EKF method. The effectiveness of the ASTSEKF method is demonstrated by utilizing it to refine and enhance the estimations of a closed-loop nonlinear autoregressive model with exogenous input (NARX) and a deep feed-forward neural network (DFFNN) utilizing deep transfer learning techniques. The Levenberg-Marquardt and adaptive moment estimation approaches are employed to address gradient issues and stabilize the networks. Battery tests are carried out at different charge-discharge rates, temperatures, complex working conditions, and aging levels. The comparative SOC results show that the proposed ASTSEKF optimizer ensures an overall maximum mean absolute error, mean square error, and root mean square error improvements of 89.82%, 91.67%, and 90.76%, respectively. Additionally, it denoises, stabilizes, optimizes, and quickly converges the final SOC with a good balance between optimal accuracy and computational complexity. In comparison to other existing methods, the proposed ASTSEKF optimizer can overcome nonlinearities encountered by the BMS under various operating conditions to provide accurate SOC estimation in EVs.