The task of extracting overlapping and nested events has received significant attention in recent times, as prior research has primarily focused on extracting flat events, overlooking the intricacies of overlapping and nested occurrences. In this work, we present a new approach to Event Extraction (EE) by reformulating it as an object detection task on a table of token pairs. Our proposed one-stage event extractor, called ODEE, can handle overlapping and nested events. The model is designed with a vertex-based tagging scheme and two auxiliary tasks of predicting the spans and types of event trigger words and argument entities, leveraging the full span information of event elements. Furthermore, in the training stage, we introduce a negative sampling method for table cells to address the imbalance problem of positive and negative table cell tags, meanwhile improving computational efficiency. Empirical evaluations demonstrate that ODEE achieves the state-of-the-art performance on three benchmarks for overlapping and nested EE (i.e., FewFC, Genia11, and Genia13). Furthermore, ODEE outperforms current state-of-the-art methods in terms of both number of parameters and inference speed, indicating its high computational efficiency. To facilitate future research in this area, the codes are publicly available at https://github.com/NingJinzhong/ODEE.