The Duke Ellington School of the Arts is now accepting applications for the coming school year. With Israel Hicks as its new principal, the former Western High School at 35th and R Streets NW offers a full four-year academic high school program bolstered by arts courses.

Students who have completed the 8th and 9th grades may request applications at 282-0123. Auditions for dance will be held from July 18 to 22, for theater July 21 and 22, for music July 25 and 26, and portfolios for visual arts applicants will be seen July 20, 21 and 22.

Learning to regulate its new airconditioning (rented), the New Playrights' Theater is previews of "Sweet and Hot, the Songs of Harold Arlen." In a cabaret setting by Russell Metheny and with beer or wine included in the ticket price, this is a long-due salute to the composer of "Over the Rainbow," "Stormy Weather" and "That Old Black Magic."

Such pals of Arlen's as Edward Jablonski, E. Y. Harburg, Robert and Wilva Breen plan in-person visits to the show to report to the composer about the Ken Bloom-Berthe Schuchat production, and there's a plan afoot for the whole company, 10 performers and three musicians, to perform in Arlen's New York living room.

Performing at Ford's between 10 a.m. and 4 p.m., the New Federal Theater will expand its offerings about Civil War Washington with evening performances the second week in August. Actors, singers, banjoists and guitarists will be needed. Contact Ramona Baker at 426-6924, ext. 6.

Director Michele Nelson is determined that the Edwin Booth Theater's production of "Oliver" will be the whammiest Bel Air ever has seen. Auditions will be held Aug. 1, 2 and 3 at 7 p.m. at Harford Community College for actors, singers and dancers. Musical director Paul E. Labe Jr. will hear musicians Aug. 3 at 8 p.m. Plans are for a company of 100 when the Lionel Bart-Charles Dickens musical opens Oct. 19. Details at 879-8920.

Geraldine Fitzgerald will be performing her "Song of the Streets" Tuesday at 8:15 p.m. in the University of Maryland's Tawes Theater on the College Park campus. The next morning at 10 she will hold an informal seminar about the varied career which has taken her from Ireland to the latest Pulitzer Prize play, 'The Shadow Box." Further details at 454-5910.

Georgetown Classical Theater, founded by Ray Reno, will present "Sir Gawain and the Green Knight" for three-weekends starting Friday at 8:30 p.m. in Stage Three, 37th and P Streets NW. There are also Saturday night performances and Sunday matinees at 2; details at 625-4960 . . ."Once upon a Mattress" will play next week through July 31 at Wayside Theater, Middletown, Va. . . STAY - Summer Theater of the Arts for Youth - will open "Fiddler on the Roof" Wednesday at the Jewish Community Center of Greater Washington, 6125 Montrose Rd., Rockville, with further performances July 21 at 12:45 p.m. and 8 p.m., July 22 at 1 p.m. and July 24 at 8:30 p.m., details at 881-0100. . .Tuesday noon the Gallery Place Mall will have a preview of the "Romeo and Juliet" balcony scene in the production opening Wednesday night at the Sylvan Theater. The 8:30 performances there will be free through Aug. 7. . . Wayne Shirley, of the Library of Congress, will discuss "Porgy and Bess" with cast members Wednesday noon at the Kennedy Center.