Exxon, Royal Dutch/Shell, Chevron, Mobil, Texaco, British Petroleum, Standard Oil of Indiana (Amoco) - these are the legendary ''seven sisters.'' At one end of the earth, employees of these multinational, ''integrated'' oil companies might be poking around a lonely desert or an icy Arctic gulf in search of oil.
At another, television commercials urge drivers to trust their cars to the man who wears the star, or to the friendly tiger, the flying horse, or the yellow seashell.
In between, the integrated oil companies maintain multibillion-dollar drilling operations, fleets of tankers, and elaborate refineries and storage depots that fuel the Western world's economy.
But although these globe-girdling companies remain powerful corporate entities, they are in the throes of great change today. At many levels of their operations, big oil companies have seen their once unassailable clout challenged:
* Important overseas oil fields have been nationalized - either gradually or overnight - in the past 20 years.
* Exploration for new oil has become at once more costly and less lucrative.
* Intense competition has arisen in the area of refined petroleum products at the same time that refineries are becoming more expensive to build, maintain, and retrofit with pollution safeguards.
* Brand-name loyalty is waning - and this may accelerate under the pending settlement of a suit brought by service station operators in which oil companies will allow retailers to sell any company's gasoline.
* And most important of all: The persistent glut of oil on world markets keeps oil prices weak. Thus the cash with which these companies were once rich - cash that went to exploration and to hefty stock dividends - is much more meager.
''The integrated oils have lost control due to market conditions,'' says Fred Leuffer of the Cyrus Lawrence securities firm in New York. ''Oil prices more than ran their course in the '70s. We have a more competitive market. It's become a tougher business in refining and marketing. The notion of a company balanced between production, refining, and retailing is fading.''
To consumers, the fate of big oil may not appear very distressing. After all, gasoline prices are moderate, and there is plenty of gasoline around.
Most energy experts see oil supplies and prices as stable throughout the 1980 s and as far as the turn of the century. At that point, the energy picture worries some analysts - but that is years away. For the overall economy, meanwhile, the decline in oil prices has been the biggest contributor to the decrease in the inflation rate over the past three years.
For investors, however, the story is different. One security analyst describes the once-hot oil company stocks as ''dullsville.'' Although the market can be shaken by a cold snap or a twist in Middle East politics, for the most part the performance of oil stocks looks bland.
Hard times have brought about an era of consolidation among the big companies. Earlier this year, Gulf was absorbed by Standard Oil of California, which is now called Chevron. Mobil and Texaco, meanwhile, also grew, absorbing Superior Oil and Getty Oil, respectively. Royal Dutch/Shell bought out Shell Oil of Houston in a similar acquisition.
Industry analysts note that the acquisition spree is the most popular tactic now being used by oil companies to build up their base of oil reserves. That is important, because financial analysts rate the strength of these companies - and thus the value of their stock - by the size, growth, or depletion of oil reserves. After all, oil in the ground is what will make the company profitable.
To enhance their financial status and bolster the value of their stock, many of the companies have determined that buying the reserves of other oil companies - or buying the other companies outright - is the least expensive way of adding to reserves, especially when one looks at the high cost of exploration and the political risks entailed in relying on oil fields in unstable areas of the world.
A recent survey by the Arthur Andersen & Co. accounting firm determined that more than 40 percent of the 375 major oil companies increased their reserves in 1983 by acquiring producing oil and gas properties or companies.
The Andersen report noted that when prices for oil and gas fell in late 1982 and 1983 this reduced cash flows to producers and also reduced the value of reserves. Debt burdens, the study said, further restricted the ability of producers to conduct exploration, and as a result new investment dropped sharply.
A weak world oil price is the sword of Damocles over the integrated oils.
According to a forecast made by the Wharton Middle East economic service, nominal oil prices will remain flat through 1986. That translates into substantial fall in ''real'' (inflation- and exchange-rate-adjusted) prices during those years.
Because it is traded in dollars, crude oil has been insulated from inflationary erosion, owing to the strength of the dollar in relation to other currencies. But Kristin S. Lindow of the Wharton service notes that by 1986 the dollar will decline. As a result, she says, real oil prices will fall 7.6 percent that year.
Economic expansion in the Western world may absorb more of the surplus oil on the market, Ms. Lindow says, but the expansion is beginning from ''a lower base'' than previous forecasts had assumed. She says alternate scenarios see a big price drop as unlikely but also recognize no real possibility of a supply disruption that could drive up prices.
Ms. Lindow agrees with assessments that by the year 2000 oil reserves in the West will have fallen significantly and consumption will be high, but points out that there are still areas of the world with potential, citing big new oil finds in Kuwait and Iraq in recent months.
For the oil industry and for oil-producing nations, the revenue prospect is bleak.
Still, there are ''nonfundamental'' ways these companies can improve their positions, says Mr. Leuffer of Cyrus Lawrence. These include acquisitions, stock buy-back programs, revamping of refineries, and the upgrading and diversification of products available at service stations (example: Texaco stations that sell groceries, too).
But from a strategic point of view, notes Mr. Leuffer, big oil companies really have only three ways to prosper: They can improve prices (a nonstarter), up unit volume (also unlikely, because of oversupply), or cut costs.
Cost cutting is the option that ''every oil company is trying,'' Leuffer says. The primary means is by ''fine tuning'' refinery networks. That means shutting down many refineries and keeping only those that can take a wide variety of crude oils and that can produce a wide variety of petroleum products.
But several developments bode ill for the future of oil refining operations. A new set of environmental rules on lead content will necessitate costly retrofitting of refineries. Meanwhile, the increase in ''downstream'' oil operations in oil-producing nations threatens costly competition.
New refineries in Saudi Arabia and Kuwait enable those countries to feed in their cheap, nationally owned crude and produce cheap petroleum products. The motives of such nations, Leuffer points out, can radically diverge from the normal profit motive of corporations.
''They don't necessarily go for good quarterly earnings progressions,'' he notes. ''They may in fact be looking for higher cash income for their countries.''
He adds that ''refined product is a very convenient way of cheating on OPEC crude oil quotas,'' since an OPEC member can always keep crude exports modest but boost the exports of refined products. If an oil producer is running a large budget deficit, it might have incentive to dump great quantities of refined products onto the market. Thus, he says, there is the potential for ''vicious competition'' in refined products.
As commodity companies, the big oils are subject to volatile jumps, he says, citing the low oil inventories and weak prices of the summer, the current near-frantic inventory rebuilding that is occurring, and the likelihood that by January inventories will be too full and demand weak. This is because ''they are always trying to hit a moving target.''
He says the key to investing in the seven sisters is to see them as long-term plays. The best of these, Leuffer adds, are Chevron, Texaco, and Standard Oil of Indiana.
Energy analyst Charles C. Cahn Jr., of the Sanford C. Bernstein & Co. securities firm in New York, sees the big oil companies as falling into three major strategic groups:
1. Royal Dutch/Shell and Standard Oil of Indiana have boosted their purchases of oil from the ''spot,'' or free, market. This insulates their refining and wholesale operations from swings in prices. Meanwhile they are concentrating oil exploration in countries that have not been drilled heavily and that have generally favorable fiscal terms. These have good long-term prospects - especially Royal Dutch/Shell.
2. Exxon has concentrated on near-term performance, with stock buy-back programs and curtailed spending on exploration. Mr. Cahn's report sees scrimping on exploration as being a problem in the long term.
3. Chevron, Mobil, and Texaco have gone the route of buying reserves other companies have found. Look for fairly fast growth because of these acquisitions, Cahn says. The danger for these firms lies in higher corporate debt, less in-the-ground exploration, and vulnerability if prices fall.
''From an investment viewpoint,'' he says in the Sanford Bernstein report, ''the risk in the oil markets is high, and an investor should demand high returns to compensate for that risk.''