According to the mainstream economics school, how are efficiency, equity and voice achieved in society? What does this school of thought have to say about the role of government and unions?

According to the mainstream economics school, efficiency, equity and voice are achieved through free market competition or the competitive forces of supply and demand. Prices in a competitive market reflect the value of what's being purchased and hence, wages in a competitive labor market, reflect the value of that labor. If competition exists, the optimal outcomes for both workers and employers are achieved. If an employer tries to pay too little or offers unsafe working conditions, workers can exercise voice by quitting and finding another employer. This encourages employers to provide equity in the workplace.
Under the mainstream economics school, the only role government should play is in preserving individual property rights and ensuring competitive markets. Labor unions play no useful role at all under this model - rather, they are an impediment to marketing competition because they act as monopolies that restrict the supply of labor and interfere with free market forces.