The strongroom key is a quest item used in the The Path of Glouphrie quest. It can be obtained by searching the mahogany chest in the north-west corner of the room reached by crawling the tunnel in the east room of the Gnome Village Dungeon.
The key is used to unlock the room west of the mahogany chest which has Yewnock's machine. A key to a chest is needed to unlock the mahogany chest. After the quest, the key is no longer needed.