None of this is legal speak. . Illegally employed workers often have no explicit contract but are somewhat protected by the laws of the land. . Other work? Unclear whether you mean other work instead of agreed or in addition to agreed. . They were required to perform duties not included in their contract. Outside of their job description, off-book duties. While employed as .... they actually worked in a role of .... In the country on a visa for restaurant workers they actually filled roles in various gentlemans' clubs. Workers may be required to perform other duties from time to time. Their actual roles in the organisation did not match the job titles nor job descriptions in their employment contracts. ... bore no resemblence to ...

In the US, when someone does a job, then the employer and the employee need to report their earnings to the government so that taxes can be paid. * "Under the table," "off the books," and "illicit employment" mean that no one is reporting that work to the government. Someone (either the employer, the employee, or both) is cheating on their taxes. * "Moonlighting" is when a person has a main job (an accountant), but then also spends some of their time working a second job (a jazz singer) somewhere else to earn more money or because they really like it. Some jobs do not let you moonlight. If they find out you're doing it, they'll fire you. * What you're talking about is doing work outside of your official duties. (Some people might say "that's not in my job description.") Generally, in the US, that isn't working "illegally" unless the thing they ask you to do is illegal. So if your employer asks you to sweep the floors - even if you are an accountant, that's not illegal (you can argue that it's outside of your job description, but they can also fire you.) If your employer asks you to kill his mother-in-law, that's illegal.

The language used will vary from place to place as it will refer to legislation in that locale.