Find the list.phtml file which gets called in the category pages.
For example: app/design/frontend/rwd/default/template/catalog/product/list.phtml
Now, add the below code where you want to show label/status
$stock = Mage::getModel('cataloginventory/stock_item')->loadByProduct($_product);
$qty = $stock->getQty();
if($qty <= 0)
<span class="out-of-stock"><span>Sold Out</span></span>
<span class="in-stock"><span>In stock</span></span>
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