How do I avoid re-listing sold items and how do I delete them from SE+ and Amazon?

The software will not automatically delete items from the local inventory database once they've been sold out. You need to acquire your orders first clicking Orders > Get my orders now.

When you do this the Inventory Quantity values will be decreased to reflect your recent sales. All Merchant fulfilled SKUs for which the quantity has been decreased to zero will also get checked in the Delete from Amazon column.

To delete the sold items from Seller Central and SE Plus first sort your inventory using Delete from Amazon and Inventory Quantity columns (after sorting by the first column press the Shift key while clicking on the second sorting column).

Next, select all items with zero quantity and which are marked for Delete from Amazon, then click Upload > Remove listings marked for delete, and choose to upload for items in your current selection. 

Once delete requests have been uploaded to Amazon just press the Delete button to remove the items from the local inventory database as well.