Two approaches:
use the sticks through the Use menu, aiming at the holes
try clicking on the holes...
It normally should work with no problems...
One approach is to check out the problem area with another save.
The file page of John Hubbard's Wizardry & Wizards and Warriors Site is at:
https://www.tk421.net/wizardry/files.shtml
It has two late-game saves:
https://www.tk421.net/wizardry/files/save-ww.zip
https://www.tk421.net/wizardry/files/save-ww3.zip
Go through the area with either save. then see how things work in the area.
Backing up existing saves is always a good idea here.
As for the Wooden Sticks:
(1) Have the item in your inventory
(2) Bring it up on the Use/Give screen
(3) Click on the relevant Stone Groll