Mark -
This is a topic that has quite a number of posts in this forum. One of these days it really should be made a sticky...
You can use matchsticks, toothpick, dowling, even wood putty to fill the holes. Essentially you are just filling up the hole with material so that when you put the screw back in, it is kind of like putting it into fresh wood. Using wood glue will help the wood filler stay there, and gives it extra strength. This is an old wood working trick that is used all the time for loose wood screws, and it should last a long time, if not forever, depending on how much tension you put on your strap buttons.
If you use a regular wood glue, if you get any on the finish, you can clean it right up with a little water on a towel.
Let the repair set up over night for maximum strength, although generally is not necessary. For gigs - if you can find some toothpicks, or matchsticks, you can do a temporary repair right there, and then use glue when you get home to make it more permanent. If the hole gets really large, probably better to get some hardwood dowel that has a snug fit, and again use the glue, and let it setup over night. The hardwood won't compress as much, and it will be much like the original wood that the strap lock was screwed into.
Good luck.
Paul