Below is the code to  load multiple categories products also you will need to join  the collection and filter to get product list. Use below code.

$productcollection = Mage::getResourceModel('catalog/product_collection')
->joinField('category_id','catalog/category_product','category_id','product_id=entity_id',null,'left')
->addAttributeToFilter('category_id', array('in' => array(4,3,2,1)))
->addAttributeToSelect('*')
->load();
foreach($productcollection as $product){
echo $product->getName()."<br/>";
echo $product->getId()."<br/>";
}

Where 4,3,2 and 1 is the category ids.