Luther Hodges Jr., who has described himself as a "banker with a social conscience," is taking on one of the toughest current challenges in the banking industry.

Starting Nov. 15, Hodges will become board chairman and chief executive officer of National Bank of Washington, the federal city's oldest and third-largest commercial bank. Given the new winds of competition sweeping through American financial institutions, just performing well in such an executive position is task enough.

But Hodges faces another, immediate challenge -- one that should draw on his varied education, business and political careers. He must help eradicate the image of a bank under improper influence and one with questionable lending practices. He must stop a decline in assets and deposits.

For a man who enjoys getting out and meeting people -- as Hodges was doing yesterday in San Francisco and on Monday in Seattle, on the stump for President Carter -- the new job will also be a welcome relief from the near-anonymity he has enjoyed for the past year as deputy secretary of Commerce, after he was turned down for the Cabinet post itself.

Hodges said yesterday his resignation from the Carter administration will take effect a week from today. Hodges said he had decided some time ago to return to the private financial sector in the near future, whether or not Carter wins.

And Hodges is returning to the business he knows best -- running a bank, as he did in the 1960s and 1970s in North Carolina, when financial institutions in that state were establishing many competitive banking trends that since have become commonplace.

Once at NBW, Hodges will seek to show consumers, employes and the city's business community that NBW is moving to a new chapter in its often-stormy history. That's a demanding job, because even veteran NBW officers had no idea until recent weeks that the controlling owners, the United Mine Workers union, influenced professional banking decisions in any significant fashion.

And Hodges starts with an additional handicap: He is an outsider in a closely-knit local business community where most bank executives have been promoted from inside after many years of work and where most business customers have been friends or acquaintances for years. Non-Washingtonians have not fared well in local bank executive suites.

But Hodges is not worried about that. "I know the Washington banks well and I have many friends among my to-be competitors," Hodges said in a telephone interview yesterday.

He arrives on the scene none to early for NBW as all financial institutions begin to scramble for business in the new world of competitive services that starts on Jan. 1, when savings and loans associations can begin offering checking accounts, and most banks and S&Ls will start paying interest on checking deposits.

Key marketing decisions and strategy decided during the next few weeks could well determine an individual bank's survival in the 1980s. NBW officials, distracted by the continuing publicity about the management decisions under UMW ownership and control, should now be free to join with Hodges in planning for the future.

"There will be lots of changes in the 1980s," Hodges said. "Good banks will prosper in the new environment, and the good and stronger savings and loans will prosper. The point is that 21,000 financial institutions (of today, nationwide ) are not necessary. There will be consolidations and changes, with regional and national banking."

Hodges said his first task inside NBW will be getting to know the customers and employes. "I expect to say very little for a while, to be listening and observing." To this general task will be added such specific requirements as hiring a new senior commercial lending officer and working out plans to reduce the number of problem loans on NBW books (some $53 million of loans have been criticized by bank regulators). These are among provisions in an extraordinary agreement yesterday with Comptroller of the Currency John Heimann under which the UMW (owner of three-quarters of the bank's stock) agreed to stop exercising control over the institution, one of the most severe disciplinary steps ever taken by banking regulators.

In turn, this has led to speculation that the union ultimately will decide to sell its bank ownership (previous approaches by foreign investors were turned down).

Still wearing his Commerce Department hat yesterday, Hodges emphasized his view that problems at NBW in recent months had been "exaggerated" and that, in any event, "they are a matter of the past." He also asserted that the difficulties were "related to a few individuals," and that the bank's other officers and employes are "as good as you can find . . . NBW has a very sound base."

Hodges, who will be 44 on Nov. 19, majored in economics at the University of North Carolina, received a master of business administration degree from Harvard University and then taught at the University of North Carolina before joining North Carolina National Bank in 1962.

At the bank, he became executive vice president in 1970, vice chairman in 1973 and board chairman from 1974 to 1977. His bank's holding company, NCNB, is the largest banking firm in the Southeast with assets of more than $6 billion compared with NBW's assets of $857 million.

Hodges left banking to seek the Democratic nomination to the U.S. Senate in 1978, to oppose Republican Jesse Helms. But the campaign was unsuccessful -- he lost out in a runoff election. He became under-secretary of Commerce in 1979.

In the interview yesterday, Hodges said he is convinced the recession has ended but that the pattern of recovery is unknown. While not pessimistic about the national economy, Hodges said the whole decade of the 1980s will be difficult.

Hodges forcast a gradual increase in international business for NBW -- "no branches overseas to compete with the giants but . . . I believe we are truly in a world economy, and it is impossible to be a good bank without being internationally sophisticated."