Understanding the responses of olive trees to drought stress is crucial for improving cultivation and developing drought-tolerant varieties. Water transport and storage within the plant is a key factor in drought-tolerance strategies. Water management can be based on a variety of factors such as stomatal control, osmoprotectant molecules, proteins and wood properties. The aim of the study was to evaluate the water management strategy under drought stress from an anatomical and biochemical point of view in three young Italian olive cultivars (Giarraffa, Leccino and Maurino) previously distinguished for their physiological and metabolomic responses. For each cultivar, 15 individuals in pots were exposed or not to 28 days of water withholding. Every 7 days, the content of sugars (including mannitol), proline, aquaporins, osmotins, and dehydrins, in leaves and stems, as well as the chemical and anatomical characteristics of the wood of the three cultivars, were analyzed. ‘Giarraffa’ reduced glucose levels and increased mannitol production, while ‘Leccino’ accumulated more proline. Both ‘Leccino’ and ‘Maurino’ increased sucrose and aquaporin levels, possibly due to their ability to remove embolisms. ‘Maurino’ and ‘Leccino’ accumulated more dehydrins and osmotins. While neither genotype nor stress affected wood chemistry, ‘Maurino’ had a higher vessel-to-xylem area ratio and a larger hydraulic diameter, which allows it to maintain a high transpiration rate but may make it more susceptible to cavitation. The results emphasized the need for an integrated approach, highlighting the importance of the relative timing and sequence of each parameter analyzed, allowing, overall, to define a “strategy” rather than a “response” to drought of each cultivar.