Characterizing left ventricular deformation and strain using 3D+time echocardiography provides useful insights into cardiac function and can be used to detect and localize myocardial injury. To achieve this, it is imperative to obtain accurate motion estimates of the left ventricle. In many strain analysis pipelines, this step is often accompanied by a separate segmentation step; however, recent works have shown both tasks to be highly related and can be complementary when optimized jointly. In this work, we present a multi-task learning network that can simultaneously segment the left ventricle and track its motion between multiple time frames. Two task-specific networks are trained using a composite loss function. Cross-stitch units combine the activations of these networks by learning shared representations between the tasks at different levels. We also propose a novel shape-consistency unit that encourages motion propagated segmentations to match directly predicted segmentations. Using a combined synthetic and in-vivo 3D echocardiography dataset, we demonstrate that our proposed model can achieve excellent estimates of left ventricular motion displacement and myocardial segmentation. Additionally, we observe strong correlation of our image-based strain measurements with crystal-based strain measurements as well as good correspondence with SPECT perfusion mappings. Finally, we demonstrate the clinical utility of the segmentation masks in estimating ejection fraction and sphericity indices that correspond well with benchmark measurements.