We propose HAROOD as a short-range FMCW radar-based human activity classifier and out-of-distribution (OOD) detector. It aims to classify human sitting, standing, and walking activities and to detect any other moving or stationary object as OOD. We introduce a two-stage network. The first stage is trained with a novel loss function that includes intermediate reconstruction loss, intermediate contrastive loss, and triplet loss. The second stage uses the first stage's output as its input and is trained with cross-entropy loss. It creates a simple classifier that performs the activity classification. On our dataset collected by 60 GHz short-range FMCW radar, we achieve an average classification accuracy of 96.51%. Also, we achieve an average AUROC of 95.04% as an OOD detector. Additionally, our extensive evaluations demonstrate the superiority of HAROOD over the state-of-the-art OOD detection methods in terms of standard OOD detection metrics.