document.createElement("script") synchronously

Is it possible to call in a .js file synchronously and then use it immediately afterward?

<script type="text/javascript">
    var head = document.getElementsByTagName('head').item(0);
    var script = document.createElement('script');
    script.setAttribute('type', 'text/javascript');
    script.setAttribute('src', 'http://mysite/my.js');
    head.appendChild(script);

    myFunction(); // Fails because it hasn't loaded from my.js yet.

    window.onload = function() {
        // Works most of the time but not all of the time.
        // Especially if my.js injects another script that contains myFunction().
        myFunction();
    };
</script>

This is simplified. In my implementation the createElement stuff is in a function. I thought about adding something to the function that could check to see if a certain variable was instantiated before returning control. But then there is still the problem of what to do when including js from another site that I have no control over.

Thoughts?

Edit:

I've accepted the best answer for now because it gives a good explanation for what's going on. But if anyone has any suggestions for how to improve this I'm open to them. Here's an example of what I'd like to do.

// Include() is a custom function to import js.
Include('my1.js');
Include('my2.js');

myFunc1('blarg');
myFunc2('bleet');

I just want to keep from having to know the internals too much and just be able to say, "I wish to use this module, and now I will use some code from it."