Sheikh is originally an old man (60+). It is a much politer way to refer to an old person (rather than saying 3ajooz as an example) so it soon became custom to use it as a form of respect
An Imaam is a leader, depending on context it can mean the leader of the prayer, the guy that usually takes care of the mosque (because he leads the prayers there), the leader of the nation, a religious leader...etc. For Shia' he has more specific requirements.

An imam is the spiritual head of a Muslim community. The imam at a mosque is simply a teacher, a learned person or a prayer leader. Every mosque has an imam and an assistant imam that takes the place of the imam if he is sick or out of town, or steps in if the imam stumbles or forgets a verse.

Sheik means teacher. It is the name given to a man admired for his piety. Sheiks are sometimes imam or preachers. They are often also chiefs, village leaders or even the leader of a large tribe or nation. Many villages have an elder spiritual leader who is regarded as the keeper of the Koran