I have an XHTML strict page that has an invisible div that is controlled by Javascript. The div is set to transparent and visible by the script and a mouseover event to make
To clear up the validation issue: noscript is only allowed in the body element, style only allowed in the head. Therefore, the latter is not allowed within the former.
On the general issue: you'll want to make the div element visible by default, then hide it via CSS + javascript. This is the 'progressive enhancement' model. I notice you say you "don't want to do this because of the flicker", but I'm not sure exactly what's causing this - chances are you can fix it, so maybe you should post that as a question.