I use superglue.
A little known fact:
Linseed & Tung Oil act as "kickers" for superglue, so when gluing old oil soaked grips, you sometimes have to work fast before it hardens.
I save my sawdust from checkering old grips. When I need to fill a hole or do some patching on damaged grips, I fill the area with the oil impregnated sawdust & then put a drop or two of superglue on it. It will set up so fast & generate so much heat that sometimes it will bubble and you can see smoke rise from it.
The patch will closely resemble the color of the grip, usually just a little darker, and after an application of Walnut stain, you can hardly see the patch.