How to block annoying twitter search widget

Don't know if this would work, but is worth a try: Adblock Plus addon for Firefox?

Perhaps find the source script and add it to the block list in Adblock Plus...

Also make sure that you have all popups disabled...

Install GreaseMonkey and install this script that I wrote for you, here is the source:

// ==UserScript==
// @name          Remove the Twitter Widget.
// @description   This will remove the Twitter Widget, everywhere.
// ==/UserScript==

(function(){
  var script = document.createElement("script");
  script.textContent = "(" + twremoval.toString() + ")();";
  document.body.appendChild(script);

  function twremoval() {
    $(function() {
      $("div.twtr-doc").remove();
    });
  }
})();