WASHINGTON--Tens of thousands of long-distance telephone callers faced delays yesterday as workers rallied and walked picket lines at American Telephone & Telegraph facilities in the nation's largest strike in three years.

The Communication Workers of America, which represents 155,000 of AT&T's unionized workers, began the strike at 12:01 a.m. yesterday after rejecting the telecommunications giant's offer of a 7 percent wage increase spread over the next three years.

The two sides resumed informal talks yesterday but at a subcommittee level. No progress in disagreements over wage levels, contracting out of work to non-union or overseas companies and new job classifications that the companuy wants was reported by either.

Meanwhile, AT&T announced yesterday afternoon an agreement with the International Brotherhood of Electrical Workers, the second largest of its employee unions with 41,000 members, on a new contract providing an 8 percent wage increase over three years.

"It's a good settlement," said AT&T spokesman Herb Linnen. "Our energies now will be directed to reaching agreement with the CWA and its membership."

IBEW officials said in telephone recordings at local union offices that the offer would be submitted to its members for a vote after June 10.

Local IBEW officials made clear in telephone recordings that its members were not on strike. Members of the two unions hold identical jobs with the company but for the most part at different locations. The previous contracts between the company and each union expired at midnight Saturday.

Linnen said IBEW-member operators reported to work yesterday for all three shifts yesterday after the CWA strike was called. About 4000 of AT&T's 36,000 union operators are IBEW members. Most of them work in New England and Pennsylvania.

Rozanne Weissman, a CWA spokesman, said her union expects IBEW members to honor its picket lines at facilities where both unions represent AT&T employees.

Telephone users attempting to place person-to-person, collect, third-number-billing or credit card long-distance calls yesterday were frequently greeted with a telephone recording advising that AT&T was experiencing a "work stoppage" and asking them to wait for the next available operator.

"We're moving to fill in the gap there," Linnen said. "There may be some delays, but our management personnel filling in behind striking operators would do the best they can to fill in."

Linnen said 10,000 management and supervisory personnel ran the company's long-distance switchboards on Sunday. Ordinarily, he said, AT&T has 12,000 operators working on Sundays.

"As far as calls going through, there have been no problems," he said. "There have been some delays in reaching operators, but that's to be expected."

But he said the company was bracing for Monday, the busiest calling day of the the week when normally 24,000 long-distance operators are on duty.

With 80 percent of the long distance telephone market, AT&T handles an average of 33 million calls daily. Because of automated direct-dialing equipment, only about 10 percent of them require the assistance of the company's 36,000 union operators, Linnen said.

The strike is not expected to disrupt local phone service, including directory assistance, repairs and residential installations. The court-ordered divestiture of AT&T in 1984 spun off those local subsidiaries into seven independent regional phone companies. Their contracts with the CWA do not expire until August 9.

AT&T officials said yesterday they will try tomorrow to reopen 26 telecommunications equipment manufacturing plants in 18 states earlier targeted for shutdown if a strike occurred.