Harassment is explicitly forbidden in Omegle’s terms and conditions. Despite this, the service goes on to include various statements designed to deflect responsibility (“Understand that human behavior is fundamentally uncontrollable”, “people you encounter on Omegle… are solely responsible for their own behaviour”).
To its credit, Omegle moderates some of its video chats. However, there are no such guarantees for text-only conversations or chats that take place in the 18+ section. Unbelievably, this service doesn’t actually have any kind of a report function. This means that, in the face of harassment, all you can really do is end the chat and move on.