An output nonlinear Wiener system is rewritten as a standard least squares form by reconstructing the input-output items of its difference equation. Multi-innovation based stochastic gradient (MISG) algorithm and its derivate algorithms are introduced to formulate identification methods of Wiener models. In order to increase the convergence performance of stochastic gradient (SG) algorithm, the scalar innovation in SG algorithm is expanded to an innovation vector which contains more information about input-output data. Furthermore, a proper forgetting factor for SG algorithm is introduced to get a faster convergence rates. The comparisons of convergence performance and estimation errors of proposed algorithms are illustrated by two numerical simulation examples.