Testing is widely recognized as an important stage of the software development lifecycle. Effective software testing can provide benefits such as bug finding, preventing regressions, and documentation. In terms of documentation, unit tests express a unit's intended functionality, as conceived by the developer. A test oracle, typically expressed as an condition, documents the intended behavior of a unit under a given test prefix. Synthesizing a functional test oracle is a challenging problem, as it must capture the intended functionality rather than the implemented functionality. In this paper, we propose TOGA (a neural method for Test Oracle GenerAtion), a unified transformer-based neural approach to infer both exceptional and assertion test oracles based on the context of the focal method. Our approach can handle units with ambiguous or missing documentation, and even units with a missing implementation. We evaluate our approach on both oracle inference accuracy and functional bug-finding. Our technique improves accuracy by 33\% over existing oracle inference approaches, achieving 96\% overall accuracy on a held out test dataset. Furthermore, we show that when integrated with a automated test generation tool (EvoSuite), our approach finds 57 real world bugs in large-scale Java programs, including 30 bugs that are not found by any other automated testing method in our evaluation.