The Washington Teachers' Union and 10 of its leaders were fined more than $340,000 yesterday for violating a court order against the union's 23day strike last month.

D.C. Superior Court Judge Gladys Kessler, who imposed the stiff fines, said all the money would have to be paid by April 16.

Kessler also asked lawyers for the union and the Washington School Board to present legal arguments in 10 days on whether she should impose additional fines that could cost the union and its leaders about $200,000 more.

Last night union president William H. Simons said he would not comment on the fines until he discussed them with his lawyer. The fine against Simons is $25,000.

In addition, Kessler levied a fine of $225,000 against the union as an organization. She imposed fines of $11,250 apiece against eight members of the union's executive committee and $5,850 against one union activist who was not on the executive board.

Kessler said the total amount of fines levied, $343,350 was based on nine days of strike activity that followed a contempt order that she issued on March 12. That order established a schedule of sharply escalating fines for each day the strike continued.

In 1972 the teachers union was fined $90,000 after a two-week strike, its only long walkout before last month. D.C. Superior Court Judge Robert Campbell later reduced the fine to $50,000 and ordered the money used for a scholarship fund.

The union begain its recent strike March 6 even though Kessler had issued a temporary restraining order the night before.

The judge issued a preliminary injunction on March 24, replcing the original order. Yesterday she said she was uncertain whether fines could be imposed for the three days the strike continued after the new injunction. She asked for legal arguments on that point.

In computing the fines, Kessler said she would not count Saturdays and Sundays as days the strike was in force because teachers could only comply with her back-to-work orders on weekdays.

Striking teachers returned to work last Thursday, a day after Kessler met a key union demand and reinstated until July 15 the union's old contract with the school board, which the board had sought to change.

The judge said the board could take "no adverse action" against strikers. She also ordered new efforts to reach a long-term contract settlement by mid-summer with the helop of a factfinding panel.

In a memo to board members yesterday, Supt. Vincent Reed said he still was uncertain whether he should carry out the contract fully, particularly its section allowing the check-off of union dues. Through the check-off the union receives about $35,000 every half-month or about $840,000 a year.

The board's new general counsel, James E. Brown, who started work Monday, issued a memorandum yesterday, contending that Kessler "grossly exceeded" her power in extending the contract. He said Reed should not resume the dues check-off until the board votes to comply with the judge's order or appeal it.

Yesterday union president Simons said there have been a few cases of "harassment" since strikers returned to work out but "no crisis problems" in carrying out the terms of the contract.

The board scheduled another meeting tomorrow, its third in a week, to discuss a possible appeal.

In her order yesterday, Kessler said the teachers' union fines should be paid directly to the Superior Court. She said she will decide later where the money ultimately will go. Under the order no individual strikers, except the union leaders named, are required to pay any fines. CAPTION: Picture, JUDGE GLADYS KESSLER . . . asks legal arguments in 10 days