Abnormalities in biological cell nuclei shapes are correlated with cell cycle stages, disease states, and various external stimuli. There have been many deep learning approaches that are being used for nuclei segmentation and analysis. In recent years, transformers have performed better than CNN methods on many computer vision tasks. One problem with many deep learning nuclei segmentation methods is acquiring large amounts of annotated nuclei data, which is generally expensive to obtain. In this paper, we propose a Transformer and CNN hybrid ensemble processing method with edge awareness for accurately segmenting abnormally shaped nuclei. We call this method Hybrid Edge Mask R-CNN (HER-CNN), which uses Mask R-CNNs with the ResNet and the Swin-Transformer to segment abnormally shaped nuclei. We add an edge awareness loss to the mask prediction step of the Mask R-CNN to better distinguish the edge difference between the abnormally shaped nuclei and typical oval nuclei. We describe an ensemble processing strategy to combine or fuse individual segmentations from the CNN and the Transformer. We introduce the use of synthetic ground truth image generation to supplement the annotated training images due to the limited amount of data. Our proposed method is compared with other segmentation methods for segmenting abnormally shaped nuclei. We also include ablation studies to show the effectiveness of the edge awareness loss and the use of synthetic ground truth images.