Your sculptural pieces will need a regular dust with a dry or lightly damp cloth. Ensure your piece is left dry.

If using your functional items for food, then I recommend following these steps:

If using as a serving piece, wipe down with a dry or slightly damp cloth and immediately dry.
Never put in dishwasher.
Never let wooden items soak in water, as it will cause the wood to expand and soften.
Apply an even coat of food-safe oil as needed using a soft cloth. Allow the oil to fully penetrate the wood's fibers overnight, then buff off any excess with a clean rag.
Over time, if you feel it is required, then work over your piece with 320 fine grit sandpaper. Sand along the direction of the grain, wipe off the dust with a clean cloth before applying an even coat or two of food-safe oil, letting it soak in between applications. Let dry overnight, then buff.
* Please note that if used, olive oil will go bad over time.