Three likable plays open, in New York; Major Barbara Comedy By George Bernard shaw. Directed by Stephen Porter.

Elizabeth and Essex Musical based on "Elizabeth the Queen," by Maxwell Anderson. Book by Michael Stewart and Mark Bramble, music by Doug Katsaros, lyrcs by Richard Engquist. Directed by Nancy Rhodes.

Several lightly pleasant melodies, a strong musical performance, and a bristling Queen Elizabeth I by Estelle Parsons comprise the main attractions of "Elizabeth and Essex," at the Encompass Theater on West 42nd Street's Theater Row. Librettists Michael Stewart and Mark Bramble have preserved the main features of Maxwell Anderson's 1930 drama about the long but ill-fated relationship between an overweeningly ambitious Earl of Essex and the much older Gloriana.

Accompanied by a very good 16-piece chamber orchestra under the baton of Jack Gaughan, Miss Parsons and company perform an operetta-style musical about love, war, and palace intrigue. At first hearing, numbers like "Gossips," "The First to Know," "Love Knots," and "All I Remember is You" made an agreeable impression.

Although always a formidable presence, Miss Parsons has not been given much range by director Nancy Rhodes. Richard White's Essex, looking like a young Errol Flynn, sings well. So does Florence Lacey as Mistress Gray. But this handsome and obviously ambi- tious production fails, even in musical-comedy terms, to create a very convincing illusion of courtly deportment in "Good Queen Bess's glorious days."