Javascript not working in a WebView Activity

You should implicitly enable Javascript execution in your WebView, since this could cause XSS and other vulnerabilities.

web = new WebView(this);
web.getSettings().setJavaScriptEnabled(true);

Also, I prefer to set my WebViewClient via

WebViewClient webViewMainWebClient = new WebViewClient()
{
   // Override page so it's load on my view only
   @Override
   public boolean shouldOverrideUrlLoading(WebView  view, String  url)
   {
       // Return true to override url loading (In this case do nothing).
       return false;
   }
}
web.setWebViewClient(this.webViewMainWebClient);

to let me restrict usage of only my sites.

Set this setting as well for your webView:

WebSettings settings = webView.getSettings();
settings.setDomStorageEnabled(true);

For Detail refer to answer in the following link: ERROR/Web Console: Uncaught TypeError: Cannot call method 'getItem' of null at http://m.youtube.com/:844

Update: or adding this might help:

webView.loadDataWithBaseURL("fake://fake.com", myString, "text/html", "UTF-8", null);