John N. Gentry, the chairman of the board of inquiry named by President Carter yesterday in the coal strike impasse, is a manpower expert who served 13 years in key positions in the Labor Department.

Gentry, 47, now is partner in a management firm with W. Willard Wirtz, a former secretary of labor. Gentry served as deputy assistant secretary under Wirtz and James D. Hodgson.

The other members of the panel are Eva Robins of New York City and Carl A. Warns of Louisville, Ky., both private arbitrators.

Gentry is a graduate of the University of Maryland and the Georgetown University Law Center. He is married and the father of two children.

Robins, 67, gained a reputation for good-humored firmness and justice while resolving labor disputes in New York City.

She was born in Hamilton, Ontario, but has lived in New York since attending St. John's Law School at night while clerking for the Borden Co., as a young woman.

After doing legal and labor relations work for Borden, she became, in 1956, the first woman mediator at the New York State Mediation Board.

In 1968 she moved to the Office of Collective Bargaining, which administers some labor laws for 300,000 municipal workers.

Robins left that post six years ago and has been in private arbitration practice since then.

Warns has been a professor of law at the University of Louisville and a consultant for Joseph E. Seagram & Sons. He holds graduate degrees from the University of Louisville and Harvard