In West Virginia, a young leukemia victim is about to get a last wish--a room of her own.

In Hampton, Va., the betting is that by 1992, someone in the East Hampton Striders Athletic Association will be an Olympics contender.

In Washington, D.C., where 650 underprivileged youths are enrolled in the Higher Achievement Program, the catchall phrase is "D.C.'s poorest but brightest."

Each of these seemingly unrelated projects has something called "volunteerism" in common, and yesterday 18 of them from around the country were rewarded at the White House with the first annual President's Volunteer Action Awards. They were presented yesterday afternoon by Nancy Reagan in her husband's absence.

Last night the recipients were feted again, this time by some of the leading figures in the Reagan administration. That occurred at the Washington Marriott Hotel black-tie dinner where Vice President George Bush delivered the keynote address.

"This nation was born out of sharing," Bush told the crowd of 400 dining on $125-a-plate dinners of artichoke neptune, filet mignon bordelaise and savarin of lime parfait. "You saw it the other day when people were sandbagging the rivers."

At the party before the dinner, some of the honorees still professed to have difficulties with the reality of recognition and the company they were keeping.

"Just a simple week," said Richard Gannon of Higher Achievement, a fifth-generation Washingtonian who had never even toured the White House much less been invited to lunch there. "I had lunch with the president's wife--and I'm getting married on Saturday."

Gannon's brother, Doug, founded the 7-year-old program whose object is to push a selected group of public school children to their maximum potential.

In the throng around the vice president was Philadelphia policeman William Sample, founder of The Sunshine Foundation, which tries to fulfill the last wishes of terminally ill children. He described for one guest the young leukemia victim.

"She, her two brothers and their parents live in a three-room house. All she wants is a room of her own," said Sample.

Earlier in the day, Mrs. Reagan presided over the White House ceremonies. She quoted from the "Wizard of Oz" in commending their "volunteer spirit" in such areas as employment, health, education, recreation and the environment.

Recalling the scene where the Tin Man is given an honorary heart, Mrs. Reagan quoted the Wizard: "Back where I come from there are men who do nothing all day but good deeds . . . their hearts are no bigger than yours. But they have one thing you haven't got: a testimonial . . . Remember, my sentimental friend, that a heart is not judged by how much you love, but by how much you are loved by others."

Though the Tiffany-made sterling silver medals she presented were not in the shape of a heart, they were "symbolic," she said, of the honorees' accomplishments.

"Let me say you, too, are loved by others . . . ," Mrs. Reagan continued.

"And this testimonial at the White House--the first of many--is a way the American people can pay tribute to you for your unselfish and humane work," she told her 150 luncheon guests in the East Room.

Recipients, selected from 2,300 nominees, included the following from Virginia, Maryland and the District of Columbia:

Lee's Friends Oncology Patients, Norfolk, Va., founded in memory of Lee Harkins, who died at age 16 of cancer, to aid cancer patients and families;

East Hampton Striders Association, Hampton, Va., which provides recreational activities for children;

Lawrence Shulman of Silver Spring, founder of three programs providing vocational education in various trades.

Higher Achievement Program, Washington, which organizes teachers and volunteers to tutor 4th-9th grade high achievers from low-income families.

Other recipients included:

The Sunshine Foundation of Philadelphia;

Teleministries USA of Harrisburg, Pa., offering a 24-hour crisis and referral service to persons in need;

International Union of Operating Engineers, Local 61, which recruited members to construct physical therapy equipment an Easter Seal rehabilitation center.

Employment Aptitude and Placement Association of Ventura, Calif., which found jobs for 2,000.

REACT International of Northbrook, Ill., which provides assistance in natural disasters.

New Directions Club Inc. of Houston, Tex., a halfway house for ex-prisoners.

Mrs. A. E. Eulert of Wichita, Kan., who pioneered and organized braille services in her community.

Elizabeth C. Titus of Shaftsbury, Vt., who founded the student conservation program in the national parks.

Arts and Humanities Council in North Dakota, which provides access to the arts for the Devils Lake, N.D., schools and community.

Jacqueline F. Merritt of Dubuque, Iowa, who organized the state's first handicapped arts festival.

Bobby Trimble of Midland, Tex., who organized volunteers to repair homes of older, disabled or low-income residents.

Homer Fahrner of Sacramento, Calif., organizer of Glaners Statewide, which collects leftover produce from farms and distributes it to the needy.

Pacific Northwest Bell of Portland, Ore., whose teams of volunteers help communities in Oregon, Washington and Lewiston, Idaho.

Tenneco Inc. of Houston, Tex., which provides volunteers for community services.