Morphological abnormalities in biological cell nuclei are used as essential features for diagnosing diseases, determining cell cycle stages, and conducting other fundamental cell biological research. While many deep learning approaches have been proposed for segmenting normal elliptical nuclei, less work has been done on segmenting abnormally shaped nuclei. One issue is that acquiring a significant number of annotated nuclei data poses a challenge for many deep learning segmentation methods, particularly due to the generally high cost associated with obtaining annotated data. The lack of the use of shape analysis is another problem that causes segmentation to not perform well for abnormally shaped nuclei. To address these problems, we propose a system to segment abnormally shaped nuclei with limited training data. We generate synthetic ground truth images of abnormally shaped nuclei to supplement the limited amount of training images available. Six Mask R-CNNs are trained to segment abnormally shaped nuclei. We then introduce an ensemble strategy, known as Weighted Mask Fusion, to combine the segmentation results from the six Mask R-CNNs. We describe a shape analysis step, based on a convexity measure, that is used on the segmented nuclei in the ensemble result to further improve the segmentation performance. Our proposed system is compared with other segmentation methods for abnormally shaped nuclei. The evaluation demonstrates the effectiveness of the ensemble processing, fusion, and convexity measures for segmenting abnormally shaped nuclei.