Thick formable epoxy putty in tubes from the home centre. Backing it with some foil or tape and reinforce it with some compatible screening if you need to. I'll second JB Weld, great all-purpose stuff.
For larger holes, plastic or metal plugs look clean but very present visually.
For RF, MasterBond, RS Components, and others have conductive epoxies to fill or overcoat, and-or use adhesive foil.