That is a common carpentry repair for stripped screw holes in wood. Don't you watch TV at all? This Old House, half the shows on HGTV and DIY network... all at one time or another show this repair. It's a good low budget way to fill 5 minutes of airtime.
Epoxy, wood glue, even crazy glue will work in a pinch. Epoxy has the advantage of being cheap, and having a version that cures completely in 5 minutes so you are not sitting around all day waiting for the glue to dry. Crazy glue is expensive if you buy the stupid little metal tubes.
If you want to be more sophisticated use hardwood dowels instead of toothpicks. Drill out the hole for the dowel, epoxy the dowel in, trim off flush with the surface, and drill a new hole in the dowel.