Boil them.
If the wood is to big to boil and the vine would be ruined I would soak them in a solution of 1 cup of household bleach (generic unscented plain bleach) to 1 gallon of water. Let them soak a for 10-15 minutes rinse, rinse, rinse, rinse.
Also might want to think about switching to fake driftwood. They make some pretty good stuff now. Much easier to keep clean.
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