Is employment in a company where some of the entrance exam materials were cheated upon permissible or forbidden, knowing that the cheated materials are unrelated to the nature of the work and that the company retrains successful applicants for two years?

You must repent to Allah for cheating in the competition. The basic principle is that you are not entitled to the job if you did not pass the competition legitimately. However, if you are qualified for the job and the company will train and qualify you, and your work does not deprive a more deserving person of an opportunity, then there is no blame upon you for working there.