Strawberry is a popular fruit with a unique flavor between sweetness and sourness. Harvesting the fruit at the correct ripeness stage, along with the estimation of its acidity and Brix values, is an essential factor in the smart farming of the fruit. While the previous works focus on the two tasks (of ripening stage classification and Brix and acidity estimation) separately, we first show that the effective estimation of acidity and Brix is possible and that the estimation of these measures can improve the ripening stage identification of strawberries as well. We assemble the estimation of the acidity and Brix measures in our proposed Cascaded Convolutional Multi-Task Deep Neural Learning (CC-MTDNL) structure accompanying the image classification task simultaneously. Our best empirical network structure achieved a 96% classification accuracy while also effectively estimating Brix and acidity values. In particular, the proposed CC-MTDNL model shows higher effectiveness when compared with other neural network models in our experiments. These findings will benefit both consumers' and farmers' perspectives for taste and more effective harvesting and grading of strawberries.