Spray them with a 10% bleach solution and rinse well. Allow items to dry before putting them in the tank. A 10% bleach solution is just 1 part bleach to 9 parts water. It's usually most convenient to have a spray bottle (can be purchased at Home Depot) for easy use. If the branches are small enough to fit in the oven, cooking them is also a good method of killing any bugs on them. Soak the wood for a while to decrease the risk of fire, then bake them at 300°F for 20 minutes.