The simplest solution to change the property for both current and future elements is to override the overflow property's value in a dynamically created stylesheet element:
var s = document.createElement('style');
s.innerHTML = '.gridArea {overflow: hidden;}';
document.querySelector('head').appendChild(s);
DEMO: http://jsbin.com/galicuto/1/edit
If you only need to change the value for a single element, you could change it via the style property:
var el = document.querySelector('.gridArea');
el.style.overflow = 'hidden';
If you want to change it for all the elements currently in the document, you can do the same, but iterate over the results given by document.querySelectorAll.