The Washington Post critics pick their favorite shows of the week. Classical Music

National Music Week which begins today, will be (as usual) a busy one in Washington. Particularly active schedules have been announced by Montgomery College in Rockville and the Washington Performing Arts Society in its lunch-hour Music in Public Places program. At least four festivals are in progress (all with free admission): a festival of American (i.e., U.S.) chamber music at the Library of Congress; a festival of American (i.e., Western Hemisphere) music mostly at the Organization of American States; a festival of American music in many forms at the National Gallery, and a festival of Washington performers (today, composer-flutist Jan Pompilo) at the Phillips Collection. Washington pianist Glenn Sales will be playing Chopin and Liszt today at the Lyceum in Alexandria.

No connection can be detected between National Music Week and the concert of traditional Japanese theater music which will be presented by the Nagauta-To-On-Kai Ensemble tonight at the Smithsonian. Other ensembles with unusual names: Sistrum, tomorrow night at Strathmore Hall; Asaph, tomorrow night in Lisner Auditorium; the Electric String Quartet Thursday noon at the World Bank.

Living American composers featured in concerts this week include: William Schuman, Tuesday night, and David Diamond,Saturday afternoon at the Library of Congress; Ellen Taafe Zwilich(with a world premiere commissioned by, of all groups, the Handel Festival Orchestra), Friday night in the Terrace Theater; Judith Shatin Allen, Monday night at Strathmore Hall; Emerson Myers, Wednesday night at the National Gallery; Jon Deak and Robert Crumb (who is getting a lot of performances currently), Saturday afternoon at the Hirshhorn; and local composers Carolyn Bock, Leonard Moses and Louis J. Reichwein, as part of the Monumental Brass Quintet, Tuesday night at the Prince George's Publick Playhouse.

Not living and not American, Johannes Brahms will nonetheless be featured in a gala, marathon birthday observance (his 153rd), Wednesday night at the German Embassy. The (ticket-buying) public is invited.

The Washington Savoyards will present Gilbert and Sullivan's "Patience," beginning Thursday evening at the Trinity Theatre in Georgetown. Peter Maag returns to the National Symphony this week with a program of Mozart and Richard Strauss. DANCE

Dancefest '86 concludes today at Glen Echo Park with performances, films, workshops and classes from morning to night. Jan Taylor Dance Theatre offers two premieres and other repertory this afternoon at the Dance Arts Moving Arts Theater. Murray Spalding Dance Theatre previews a multimedia work-in-progress, "Tables, Titterings, and Travels," tonight and Monday at the 443 I Street Space. The Dance Place series continues with Donald Byrd/The Group, a New York troupe presenting "A Formal Response," an evening-length multimedia work, at Montgomery College's Performing Arts Center Saturday night. The Center Dance Ensemble presents two premieres by artistic director Frances Cohen, as well as works by Alvin Mayes and Daniel West, at the Jewish Community Center Saturday and Sunday evenings.

POP MUSIC

*It may seem like an odd couple, but guitarist Pat Metheny and jazz avatar Ornette Coleman have come up with a vibrant update on the flow of innovation that began in free jazz and harmolodics. They perform tomorrow at Lisner. It's still odd to see him around the corner from the club that bore his name, but guitarist Charlie Byrd is on familiar ground at Blues Alley, where he performs Tuesday through Sunday.

Who's gonna fill his shoes? Well, don't worry about it for a while, just go to see that genuine country legend George Jones on Friday at the Patriot Center, with hot stuff Janie Fricke as opener. THEATER

*For a big, splashy show-business musical, Michael Bennett's production of "Dreamgirls" (at the National Theatre) fits the bill. "Christmas on Mars" (at the Woolly Mammoth Theatre) is the equivalent of a mad bobsled ride. Playwright Harry Kondoleon skewers the multiple neuroses of four urban residents, trying to make a nest out of an empty apartment. Both funny and painful, this is the most original offering in town right now and Woolly Mammoth serves it up with farcical zest.