How to execute code before window.load and after DOM has been loaded?

Basically, you're looking for this:

document.onreadystatechange = function(e)
{
    if (document.readyState === 'complete')
    {
        //dom is ready, window.onload fires later
    }
};
window.onload = function(e)
{
    //document.readyState will be complete, it's one of the requirements for the window.onload event to be fired
    //do stuff for when everything is loaded
};

see MDN for more details.

Do keep in mind that the DOM might be loaded here, but that doesn't mean that the external js file has been loaded, so you might not have access to all the functions/objects that are defined in that script. If you want to check for that, you'll have to use window.onload, to ensure that all external resources have been loaded, too.

So, basically, in your external script, you'll be needing 2 event handlers: one for the readystatechange, which does what you need to be done on DOMready, and a window.onload, which will, by definition, be fired after the document is ready. (this checks if the page is fully loaded).
Just so you know, in IE<9 window.onload causes a memory leak (because the DOM and the JScript engine are two separate entities, the window object never gets unloaded fully, and the listener isn't GC'ed). There is a way to fix this, which I've posted here, it's quite verbose, though, but just so you know...

If you want something to be done right away without waiting for any event then you can just do it in the JavaScript - you don't have to do anything for your code to run right away, just don't do anything that would make your code wait. So it's actually easier than waiting for events.

For example if you have this HTML:

<div id=one></div>
<script src="your-script.js"></script>
<div id=two></div>

then whatever code is in your-script.js will be run after the div with id=one but before the div with id=two is parsed. Just don't register event callbacks but do what you need right away in your JavaScript.