Most of the nation's rail service ground to a halt yesterday as the railroad clerks union expanded a 2-month-old strike against the Norfolk and Western Railway to 43 other lines across the country.

Within hours after pickets appeared at switching yards about 5 a.m., two-thirds of the country's rail capacity was paralyzed, stranding thousands of commuters and millions of tons of freight.

Service approached normal only in the Northeast, where union pickets avoided the heavily traveled Boston-to-Washington Amtrak passenger line, which is owned by the government, and the Conrail freight system, which obtained an antistrike injunction last weekend.

By late afternoon, temporary injunctions to stop the picketing had been obtained by a number of the struck railroads, including two of the largest, the Burlington Northern and the Union Pacific.

Industry officials expressed hope that similar court orders would end the picketing by today, but officials of the striking Brotherhood of Railway and Airline Clerks (BRAC) were non-committal about whether they would immediately order their members back to work. "The union officers and attorneys are carefully evaluating the situation," a union spokesman said.

But the legal situation was clouded when Chief Justice Warren E. Burger freed BRAC - temporarily at least - to shut down a total of 73 railroads over a related issue not directly involved in yesterday's strike activity.

The strike was the nearest thing to a nationwide rail walkout since a two-day strike by signalmen in 1971. A long strike, although a rarity in the industry, would have the potential for serious economic disruption, because the railroads carry about 70 per cent of the nation's freight, more than 800 billion tons of it a year. They serve as the country's main mover of coal, chemicals, autos, grain and other foodstuffs, according to an industry official.

About 4,600 BRAC members struck the N&W July 10 in a dispute over union jurisdiction and employment security, and other unions honored the clerks' picket lines.

The 235-000-member clerks union has been sporadically picketing lines that have been handling goods for the N&W during the strike, but did not move toward a national shutdown until talks broke down last week. One stumbling block was a company offer to provide permanently laid-off workers with income and benefits protection for five years, which BRAC rejected as inferior to other industry security plans.

BRAC President Fred J. Kroll said in a statement yesterday that the picketing was expanded "in order to bring increasing pressure on the N&W to start negotiating a settlement in good faith." He accused the N&W of having "maintained an aloof and arrogant position" thoughout the negotiations, which company spokesmen denied.

The dispute, hich has been going on for nearly two years, is separate from negotiations for a new three-year national rail contract governing wages and other economic issues.

On that too, however, BRAC is resisting a tentative agreement approved by some other rail unions, and has asked that a bargaining impasse be declared so it could strike in 90 days.

The National Mediation Board, which handles railroad labor disputes, has refused to do this, and BRAC has sued to force the board to do so.

The situation has led to speculation that the N&W dispute has become the vehicle for a nationwide strike that BRAC is effectively denied by the complex procedures of the National Railway Labor Act.

Yesterday's rash of picketing which came as something of a suprise despite days of speculation about BRAC's intentions, succeeded in idling between 300,000 and 350,000 of the nation's roughly 500,000 railroad workers, according to union and industry officials.

The American Association of Railroads reported a shutdown of 123,000 miles of track, more than 60 percent of the nation's total rail system. The amount of tonnage handled was reduced to about one-third of normal, the association said.

At least 100,000 morning commuters were stranded, mainly in the Chicago area, which was hardest hit.

Amtrak said about half its 52,000 daily riders were denied service although passenger trains continued to operate in the Northwest, where Amtrak owns its own tracks rather than using tracks owned by private companies.

Although the government-subsidized Conrail system, the nation's largest freight carrier, was not picketed, a Congrail spokesman said that 65 per cent of its volume would eventually be affected by a strike because of interconnections with struck lines.

Most but not all of the major railroads were struck.

BRAC's picketing was aimed at railroads that connect, or "interchange," with the N&W, carrying goods for the struck railroad while it is reduced to about 25 per cent of its normal capacity by the BRAC walkout.

Chief Justice Burger's action yesterday related to another potential falsh point for BRAC picketing: a mutual-aid pact under which 73 other railroads have been contributing $800,000 a day to the N&W during the strike.

Burger vacated a lower court order that banned picketing on the mutual-aid issue, leaving BRAC free to do so, although there was no immediate word from the union as to whether it would further escalate its picketing.

The raidroads had asked Burger to continue the picketing ban while the Supreme Court considers the legality of picketing over the mutual-aid compact.

BRAC President Kroll said last night that Burger's action "increases the number of our options for action," which he said, would be taken "at the proper time . . . within the law and in the best interests of railway labor generally."

The White House was reported to be monitoring the situation closely, and Labor Secretary Ray Marshall met with both union and industry officials.

But a Department of Transportation official said no government action was likely until the impact of the injunctions could be assessed, probably later today.