同事 is the most common, plain one. it simply means people you work with or people in the same company as you do. It could be used no matter it is a everyday conversation, a quite formal business meeting or a HR policy notice.
同儕（同侪） means peers or fellows. Strictly it should be used to refer people in the same generation of you, i.e. siblings or cousins. Nowadays, it is often used in the workplace or other contexts when a sense of fraternity is preferable.
同僚 also means colleague. But it's more often used in politic settings in the old times. Nowadays, it can be used in the workplace in general but I feel such usage is more common in Taiwan or Hong Kong than the mainland. Personally, it feels it's more appropriate for two managers call each other that than two interns do. Or you can say this one is more fancy than 同事.
Additionally, there is another word 同仁 which equals to 同人 also means colleague. They mean to refer the people who share something in common with you professionally. E.g. works in the same company or occupation. And it is a respectful term with a sense of fraternity. But it more often to be used as a collective term for a group of people rather than a specific person. So 一个同仁 is not very common.