* Swinging on a Star (The Music Box): This musical revue, previously produced at New Jersey's George Street Playhouse and the Goodspeed Opera House, celebrates the career of lyricist Johnny Burke (1908-1964). Burke, along with such collaborators as Jimmy Van Heusen and Errol Garner, was responsible for classics like ''What's New,'' ''Moonlight Becomes You,'' and ''Pennies From Heaven.'' A talented cast delivers more than three dozen numbers, grouped in thematic sections (''USO Show,'' ''Radio Show,'' a take-off on the Hope-Crosby ''Road'' movies, etc.) in delightful fashion, although the show could benefit from sharper editing.
(Belasco Theatre): Diane Shaffer's Broadway play deals with the issue of whether women should be ordained as priests in the Roman Catholic Church. It details the conflict between Sister Grace, a ''renegade nun'' played by Ellen Burstyn, and the church hierarchy, personfied by Cardinal King (Herb Foster). Another important element is Sister Grace's relationship with Ramon, a young street kid who, under her tutelage, overcomes his bitter feelings about the Church and becomes a priest. ''Sacrilege'' has a heavy-handedness and a tendency towards cliche in its characterizations, and Shaffer's blending of drama and important religious issues is none too subtle. But any play dealing with serious ideas is welcome, and the piece is grippingly acted, with Giancarlo Esposito as a powerful Ramon.
* Pomp Duck and Circumstance
(DeWitt Clinton Park): One of the more unusual theatrical events to hit New York, this is a sort of demented dinner theater (costing $150 a person), combining gourmet food with off-the-wall comedy and circus-style entertainment. ''Pomp,'' located in a mirrored tent set up in a corner of a public park, features dozens of performers enacting a topsy-turvy world. In that world, an elegant restaurant seems to be zooming out of control, with the shenanigans punctuated by various bizarre musical and circus acts. A hit in Europe, the show will travel to Las Vegas.