This winter with its cold weather and extraordinary heating bills has brought energy shock to the Washington area as never before. From the large houses of McLean to the rundown apartments of the inner city, people who hoped they had already seen the worst are reeling under the impact of new higher heating oil and natural gas prices.

For many of the well-to-do, who can fight these costs by trimming vacations and restaurant meals, there is understanding accompanied by a kind of vague apprehension; for much of the middle class, incredulity and anger; for the aged, infirm and poor, the people on fixed incomes, there is shock and even fear.

"If it keep this up, I'll have to sell the house to heat it," said Herman Stroman, a retired school janitor whose$222 oil heat bill for a recent two-week period came to more than half his monthly income.

Gladys Robinson, a retired government cook who received a $200 natural gas bill for January, said that if energy price trends continue, "I don't know how I'm going to live."

Our standard of living is definitely dropping," said Barbara Coleman, a dentist's wife in McLean.

People are coping with higher prices by installing wood stoves, wearing long johns all day, thoroughly insulating their homes when they can afford it and, of course, turning down the heat. Some say they are thinking seriously of moving south. Owners of big buildings downtown, increasingly unable to pass through higher heating bills to their tenants without losing them, are hiring energy consultants and installingcomputers to monitor and control energy use.

Basic statistics tell the grim tale: a gallon of home heating oil in the Washington area now costs $1.29, up 24 percent since last fall, according to a survey by The Washington Post. Washington Gas Light Co. says that its prices in the area went up 20 percent from 1979 to 1980, increasing the average annual natural gas bill here from $584 to $700.

It remains considerably cheaper to heat with gas than with oil becuase gas prices remain artificially low under federal price controls. But the Reagan administration, which completed the decontrol of oil Jan. 28, may seek to eliminate gas controls in September. That could double natural gas prices. Electric resistance heating is the most expensive of all, although heat pumps can be relatively economical.

Interviews connducted during the pastweek throughtout the region indicate that people may not understand the fine points of oil decontrol and possible natural gas deregulation, but they know for sure that both mean higher prices and they think they know whom to blame: the oil company and the new Reagan administration.

"My last gas bill was $100 and some,"said George Frisby, who owns a pleasant three-bedroom house in Prince George's County."Who runs this country, the Mafia? They squeezeyou all they can. It's like they don't want anybody to make it. If theyderegulate this [natural gas], good gracious . . . ."

A neighbor, Florence Rosser, said Reagan "was crazy for deregulating [oil]. How much money does the president of Exxon get? Chop off those big salaries!"

The poor feel the impact of rising energy prices far more than the middle class or the well-to-do. According to U.S. Energy Department figures printed in the National Journal, energy expenditures of low-income people consume up to 47 percent of their total incomes. For middle-income people, the figure is 25 percent or less. In both cases, the figures are roughly double what they were in 1978.

Heating oil distributors in the Washington area have have tightened their credit procedures, many demanding payment on delivery. Rolife Robertson of Quarles-Robertson Oil Inc. said that 25 percent of his customers in affluent Fairfax County are now askingto have their oil payments deferred.

"The average customers's bill for January was $350, to 400," said Robertson. "Nobody got by with one delivery, some got three deliveries. Come April or May we'll have a hell of a lot of big accounts receivable."

I swear I don't see how the people in the inner city can do it," said William T. Higgins of U-Save Oil, a small firm that serves mostly inner city apartment buildings. "Hell, they're just not buying it the way they were. most of 'em turn their [gas] ovens on."

Higgins, like the executives of many other oil distributing firms, has to demand cash on the barrelhead."Some people I gave credit to I now have on a load-to-load basis," he said.

Adam Thomas who runs another small firm, District Line Fuel Co. in Northeast Washington, said he had to cut out his budget plan under which customers could pay for their oil in equal monthly installments spread over the year because prices were risingso unpredictably that he could not accurately determine what the monthly payment should be. When it had to be raised sharply during the year, his customers complained.

Stroman, the retired janitor, lives alone in a three-bedroom brick row house at 917 Sixth St. NE. His combined income from Social Security and the District of Columbia school system, his former employer, is $420 a month. On his dresser on a recent afternoon was a bill from the Colonial Fuel Co. for $222.82 for oil that he used up over a two-week period.

Stroman plans to pay the bill, but it will be tough. "I'm just making out.

If I had somebody else living with me, I couldn't make it. If I didn't own this house [free and clear], I couldn't make it. I cuts it plenty close but I makes it. I ain't no drinker and I don't shoot no dice."

Stroman harbors the unrealistic hope that, while oil prices are going up now, they will "jump down after a while," as he put it.

Nearby, a Hessick oil truck was pumping oil into a big brick house divided into apartments. The driver, Earl Brown, said he was pumping in 100 gallons. "A hundred gallons is nothing, it won't last long," he said. "I was at this house last week and put in 100 gallons."

At the front door, 75-year-old Richard Clackley stood in the cold clutching in one hand a money order for$142.49 to pay the shared oil bill for himself and his fellow tenant. As it turned out, that was 20 cents short of what he needed and he had to scrounge for the change.

It's eating me up," said Clackley.

Inside, Rosa Stroud, 74, said, "A week ago we paid $131.69. This week we had to pay $142.49. You know, that's ridiculous."

Clackley and Stroud live in separate apartments in the house. Their circumstances are similar: they are living on the desperate edge. Stroud gets $223 a month in Social Security, out of which she pays $114 a month rent, plus her own electricity, gas for the stove and oil bills. Clackley, a retired construction worker, gets $399.50 in Social Security and pays the same rent.

Buying oil a week at a time, they are scraping the bottom of the barrel. They say they can't go on like this. Their apartments are old and in need of repair. Clackley had the gas stove burners on when the oil was being delivered to provide a little heat because the house had been without oil since the night before when it ran out.

Warmer weather may come along and save them, but Stroud now says she is thinking of leaving town. "My family is down south," she said. "They been trying to get me to go down there and if this keeps up I'll go."

Milton Werthmann, a pediatrician who lives in McLean, said his family will dine at restaurants less often and will eat cheaper cuts of meat at home has bill, which read $183 last month.

Werthmann said he has installed solar energy panels on the roof of his $200,000 home to heat the family's hot water. He has installed storm windows and doors and has "toyed with the idea" of putting in a wood stove to help cut down on natural gas use.

A large split-level home in Oxon Hill owned by Charlie and Nellie Thorne is equipped with gas central heating that is rarely used because the Thornes bricked up the fireplace in their family room last September and installed a $300 wood-burning stove. Result: a gas bill of only $24.91 for January, a very cold month.

"We keep our thermostat set at 58 degrees -- just high enough to keep the plants from freezing," said Nellie Thorne, whose husband is a custodian in the Prince George's County school system."But with the stove, we have more than enough heat for cooking and keeping the house warm."

Thorne said the family uses free wood from construction sites where her husband, equipeed with a chain saw and a small pickup, searches for wood on weekends.

Norman Coleman, a dentist, and his wife, Barbara, of McLean bought two $520 wood stoves last fall, hoping to drastically reduce the family's consumption of natural gas.

Routinely, the Colemans keep their thermostat set at between 55 and 60 degrees at night and turned off during the day. Family members were thermal underwear, heavy wool socks and jackets inside the house and the two large front doors are left open on sunny days so that the light beaming through the storm door glass can warm the foyer.

Although this January was 33 percent colder that last January, they managed to cut gas consumption by 18 percent through all these efforts -- and their gas bill was still $4 higher than a year ago. Not to mention the fact that they used up the family's collection of three cords of "mostly rotten" wood and purchased another cord for $90.

"Our standard of living is definitely dropping," Barbara Coleman said this week. "But I guess I shouldn't complain. We're still doing great compared to a lot of other people."

Theodosia Miller and husband, Robert, said they were shocked in January when they received their first natural gas bill for more than $100. The Millers, who are both retired, said they had taken special care to winterize their five-bedroom rambler in Silver Spring to head off high fuel bills.

They have installed insulation, put on storm windows and doors, covered their house with aluminum siding and they keep their thermostat set at 65 degrees. Still their gas bill for January came to $108.

"We're doing all we can now to conserve energy and still our bill is going up," said Robert Miller. "But the big question is where will it end?"

In an effort to compensate in the family budget for the rising fuel prices, Miller said he and his wife have decided to buy fewer new clothes, be content with at-home entertainment, and eat fewer meals out."

Rosa L. Barksdale was shocked last week when she received a gas bill for $338 for the period between late December and late January at her two-bedroom apartment over Al's Shoe Shine parlor at 11th and U streets NW.

Barksdale, who received a $225 monthly welfare check and pays $114 in rent, registered an anguished protest with Washington Gas Light, which sent out investigators who confirmed that the billing was proper and found that her filter system was completely clogged. They also found that she occasionally sleeps with a window partly open.

With the help of social workers of the United Planning Organization's Center Number Two, Barksdale applied for financial assistance from the D.C. Energy Office.

Shirley Brower, program manager in the energy office, said that under a four-point formula used by the city to determine eligibility Barksdale is entitled to $160 in financial assistance this winter. The gas company has agreed to help Barksdale work out a payment plan to pay the balance.

Brower said that Barksdale is one of 4,000 D.C. residents who have applied for energy assistance. About 3,500 of the applicants have already received aid averaging $250 to $300.

For Barksdale, 44, who lives with her 12-year-old daughter, the assistance has helped calm her fears, but they remain. "I need the gas for heat, but there's no way that I can pay the gas bills," she said. "I have a hard enough time just trying to keep some food on the table."