Carb cleaner is a solvent and will remove the grease, grime and crud. Use that first then separate out the steel parts that are rusted for additional treatment.
If at all possible, leave the throttle shafts intact by NOT unscrewing the two screws at each throttle plate. The plates are carefully positioned at the factory then after the screws tightened, the ends are pressed in to prevent them from backing out. Nothing worse than having your engine swallow a screw, then have the plate hang up at high engine speed. Use a wire brush on a dremel to clean these steel plates up, followed by detergent and hot water, then rinse and dry with a clean paper towel. Finally, use a light spray of carb cleaner to absorb and remove all the remaining moisture.
Rust on small steel parts like linkages and screws can be removed easily using Muriatic acid. NOT for brass and aluminum. Follow all precautions. I like to use disposable glad ware, disposable nitrile gloves and do it outside with the wind behind me. Do not soak for more than 30 seconds or so, agitate, then remove from the bath and immediately soak in detergent and water, then rinse and dry.