Setting the onclick event to a custom function results in syntax error

You were setting the actual textual element's attribute string using setAttribute, which in turn is auto-wrapped in a function!
Also, if it would have worked, there would be no body to click on once the image had disappeared.

Here is a working example you should not use, just intended to explain above statement:

Here is a function func which is converted to string (and where a string is expected, javascript usually calls the .toString() method automatically, I put it in to clearly show what happened).
Then, to prevent a quoting problem (you used double-quotes in html and for some (in my opinion, insane) reason some browsers replace single quotes in javascript to double quotes (and I've even witnessed some pre-compiling in some browsers)), I naively (because it was safe for this particular function) replaced all double quotes to single quotes.
Then we still need to remove function(){ and trailing }.
Now we arrived at the function string, which we can pass.
Finally the browser sets the actual textual attribute and wraps the code again inside a function so that it works.

<img id="img" class="std" src="http://www.free-animated-pictures.com/bug_crawls_on_screen.gif" />
intentional text filler, otherwise body shrinks to 0*0 px leaving nothing to click on...
<script type='text/javascript'>
var func = function(){ 
    var i = document.getElementById('img');
    if(i.className === 'std'){
        i.className = 'hid';
        i.style.display = 'none';
    }
    else if(i.className === 'hid'){
        i.className = 'std';
        i.style.display = 'block';
    }
};

document.body.setAttribute( 'onclick'
                          , func.toString()
                                .replace(/\"/g,'\'')
                                .replace(/^function *\( *\) *{/,'')
                                .replace(/} *$/,'')
                          );
</script>

Solution is obviously to document.body.onclick=func directly (as gillesc already commented), or use document.body.addEventListener('click',func,false) (which is what you are probably confused with).

Note that for backward compatibility (notably < IE9) you'd need attachEvent, here is a basic workaround:

function addEventHandler(elem, eventType, handler) {
 if (elem.addEventListener)
     elem.addEventListener (eventType,handler,false);
 else if (elem.attachEvent)
     elem.attachEvent ('on'+eventType,handler); 
}