The Japanese beetle has invaded Washington and the eastern United States in the largest numbers in five summers, annoying farmers and homeowners whose crops and gardens are beset with the metallic green pest.

The Japanese beetle, which first entered the United States at the beginning of the century, has an appetite for more than 300 types of plants.

In most years, the beetle is expected to eat its way through $25 million worth of crops. But this year, plant experts at the U.S. Department of Agriculture predict it will exceed previous damage and they are concerned that the beetles may finally reach California and its $14 billion agriculture industry.

The large number of beetles was caused by favorable conditions in June 1981 when females laid eggs, according to Betsy Adams, of the USDA's plant protection division. A mild spring also made it possible for a largenumber of beetle grubs to survive to maturity, she said.

Across metropolitan Washington, lawn and garden stores have recorded a dramatic leap in the sales of any kind of trap that will keep the insects from devouring roses, fruits, leaves and vegetables. At the Hechinger's store in Fairfax, a sale on Japanese beetle traps resulted in a two day sell-out and a 60-person-long waiting list for the next shipment. In many neighborhoods, rows of four-foot high traps that lure Japanese beetles into plastic bags have become common yard fixtures.

Because Japanese beetles also find large metal objects enticing, USDA officials have ordered--for the first time in five years-- daily sprayings of airplanes and installations of beetle barriers on cargo hatches at Dulles International Airport, Baltimore-Washington International Airport and four other airports and Air Force bases in Delaware, New Jersey and Ohio. Spraying began Friday at Dulles and had been in place since June at the other airports. Plans to expand the spraying to other airports, including National Airport, are being considered by the USDA.

"Japanese beetle numbers have become so high that we've been forced to impose regulations so departing planes won't carry beetles with them," said Gary Moorehead of the USDA's plant protection department. "If we find beetles flying around an airport, we have the airlines treat the vegetation around the airport. If that doesn't work, we have to resort to the chemical means of keeping beetles off the aircraft."

In 1977, the last time the USDA enforced such large-scale sprayings, disputes between the airlines and the USDA resulted in some airlines refusing to spray their airplanes. The airlines refused to use the DDT insecticide ordered by the government because of possible harm to passengers. It could not be determined what poison is being used to spray the airplanes currently.

The beetles can latch onto airplane landing gear, flaps and even on passengers' clothing and baggage, Moorehead said. If the beetle landed on the West Coast, the scenario that could result makes California agriculture officials shudder.

"Our agriculture crops would be ruined; our grape crops would be decimated, our fruits and vegetables crops would be critically damaged," said Jim Stohl, manager of the plant industry division of the California Department of Food and Agriculture. "We are projecting if the Japanese beetle reached California, it would cost the state a minimum of $1.25 million to eradicate it in each limited area it appeared."

This summer, as usual, California airports are sprayed as a preventive measure against the beetle, Stohl said.

Although scientists in the past have proclaimed an end to the Japanese beetle because of developments in traps and poisons, each year the beetle has returned. Morehead, of the USDA, said the end of the beetle season should come in late September.