Is it permissible for an employee to sell his American company's shares after three years of employment, or to postpone selling them out of desire for their increase, knowing that the company sometimes deals with usurious banks?

There is no impediment to acquiring these mixed shares, because the Prophet, peace and blessings be upon him, accepted gifts from the Jews, and they were people of usury. However, one must dispose of them immediately upon being able to, to avoid dealing with mixed funds.