It is necessary to do this one page at a time, unfortunately. Please set your inventory view to the maximum of 100 inventory items per page, using the drop-down box at the top right of your list of inventory. Then use the "Select All" button at the bottom left of your list of inventory to select all of the items on the page prior to clicking the "Delete" button.
The inventory items are sorted in the order in which they have last been edited, so the larger the page number (further back in inventory they are) the older they are.
Obviously if you edit an older item it would be near the front of the list, but otherwise they are newest to oldest.
