Using Javascript bridge in android

Your methods inside WebAppInterface class are missing the @JavascriptInterface annotation.

Your WebAppInterface class should be like this,

public class WebAppInterface {
    Context mContext;

    WebAppInterface(Context c) {
        mContext = c;
    }

    @JavascriptInterface
    public void showToast(String toast) {
    }

    @JavascriptInterface
    public void showDialog(String dialogMsg){
    }

    @JavascriptInterface
    public void moveToNextScreen(){
    }

}

Edit

Don't forget to limit your app to API17+ when loading web content into the WebView, otherwise your App will be vulnerable to attacks. Read @Robert's comment below.