Deep neural networks have achieved excellent cell or nucleus quantification performance in microscopy images, but they often suffer from performance degradation when applied to cross-modality imaging data. Unsupervised domain adaptation (UDA) based on generative adversarial networks (GANs) has recently improved the performance of cross-modality medical image quantification. However, current GAN-based UDA methods typically require abundant target data for model training, which is often very expensive or even impossible to obtain for real applications. In this paper, we study a more realistic yet challenging UDA situation, where (unlabeled) target training data is limited and previous work seldom delves into cell identification. We first enhance a dual GAN with task-specific modeling, which provides additional supervision signals to assist with generator learning. We explore both single-directional and bidirectional task-augmented GANs for domain adaptation. Then, we further improve the GAN by introducing a differentiable, stochastic data augmentation module to explicitly reduce discriminator overfitting. We examine source-, target-, and dual-domain data augmentation for GAN enhancement, as well as joint task and data augmentation in a unified GAN-based UDA framework. We evaluate the framework for cell detection on multiple public and in-house microscopy image datasets, which are acquired with different imaging modalities, staining protocols and/or tissue preparations. The experiments demonstrate that our method significantly boosts performance when compared with the reference baseline, and it is superior to or on par with fully supervised models that are trained with real target annotations. In addition, our method outperforms recent state-of-the-art UDA approaches by a large margin on different datasets.