I would argue that bringing together diverse groups of individuals is a job for the human resources department. One of the simplest strategies would be to facilitate team building activities and other opportunities for these diverse individuals to spend time together outside of the working environment, thereby getting to know and understand one another.
Another important element to consider is that cultural differences should be acknowledge and respected. Some employees may react differently to conflict or be less likely to speak up due to cultural concerns. Ground rules should be set to ensure that every member of the team understands what is expected of them. I would argue that having clearly defined expectations is one of the most important strategies in getting different personalities to work together.
Fostering a corporate culture of respect is another critical component of creating a harmonious and productive work environment. This involves ensuring that one set of values is never imposed on someone who may be from a different socio-cultural environment. This culture of respect will make it easier for members of the team who may be reserved or culturally unaccustomed to speaking up to share their ideas.
Hiring the right people also plays a role in ensuring the cohesiveness of a team. If a team member is passionate about their role within an organization, then working together to achieve their targets or goals will be in their interest.