You question is extremely broad. You're asking about the class of all SDEs. I'm assuming that you're interested in numerically integrating some form of SDE in order to estimate parameters. 

A comprehensive introduction to the subject of SDE integration is Kloeden & Platen's book [Numerical Solution of Stochastic Differential Equations](http://books.google.com/books/about/Numerical_Solution_of_Stochastic_Differe.html?id=BCvtssom1CMC), which, style- and code-wise is a bit dated now, but is still good. For the Matlab user, another fine (and shorter) introduction is this paper:

> Desmond J. Higham, 2001, An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, SIAM Rev. (Educ. Sect.), 43 525–46. [http://dx.doi.org/10.1137/S0036144500378302](http://dx.doi.org/10.1137/S0036144500378302)

The demonstration Matlab files listed in the paper can be found [here](https://www.maths.ed.ac.uk/~dhigham/algfiles.html) now.

Best method? Like with ODEs, *there is no best method*. It depends on the system. Adaptive step-size Runge-Kutta methods work for a huge class of ODE problems, but SDEs, with their noise/diffusion term, are more complicated. Without knowing anything about your system (the diffusion function $\sigma(x_t,\theta,t)$ in particular) or what stochastic formulation you're using, I can't say much. To start, use the [Euler-Maruyama](http://en.wikipedia.org/wiki/Euler-Maruyama_method) method if you have an [Itô SDE](http://en.wikipedia.org/wiki/Stochastic_differential_equation) or additive noise (i.e., the diffusion does not depend on the state variable, $\sigma(x_t,\theta,t) = \sigma(\theta,t)$) and the Euler-Heun method if you have a Stratonovich-formulated SDE with non-additive noise. These are the workhorses. Higher-order schemes are trickier to implement and are usually designed for particular types of systems/noise.

Finally, if you want a Matlab Toolbox that is still under active development, is much faster, and will be easy to use if you've ever used Matlab's ODE suite (e.g., `ode45`), try my [SDETools Matlab Toolbox for the Numerical Solution of Stochastic Differential Equations](https://github.com/horchler/SDETools) hosted on GitHub.