The Senate acted yesterday to curtail drastically diplomatic immunity for all foreign embassy personnel except ambassadors and their families.

The bill approved by the Senate would make, for the first time, thousands of foreign embassy employes and servants subject to American criminal law and civil suits.

The Senate bill is similar to one passed by the House last year. But the Senate bill also would be diplomats and their families to carry liability insurance, and would force the insurance companies to pay victims of diplomats' negligence. Previously, even if a diplomat carried insurance, some companies refused to pay victims because the diplomats were immune from civil suit.

A spokesman for Sen. Paul Sarbanes (D-Md.), who cosponsored the bill, said he expected the House and Senate to come to an agreement on the language of the bills before final adjournment in mid-October.

The new bill, if finally approved and signed by the president would repeal the 1790 law that extended full diplomatic immunity from civil and criminal prosecution to all those attached to foreign missions.

At that time, there were only a handful of diplomats in this country, and all those attached to the missions were engaged in actual dealings with the U.S. government.

As the staffs grew the old definitions of the 1970 law became outdated as more and more embassy personnel performed functions, not related to dealings with the U.S. government.

The new bill, recognizing that, draws different levels of immunity for various members of the missions. Immunity from civil actions for lower-ranking mission employes would be limited to their official functions. Immunity from criminal prosecution would remain intact.

Household servants would be stripped of all legal immunity.

Immunity for diplomats and their embassy staffs here has long been a source of concern, irritation, and occasionally, outrage on the part of nondiplomatic residents of the Washington area.

For years wary motorists have been especially cautious when they found themselves sharing the same road as a car bearing diplomatic license plates. This is because immunity laws protect embassy officials and employes from any liability in the event of an automobile accident.

What has been regarded as one of the most flagrant abuses of diplomatic immunity occurred in April 1974, when a cultural attache for the Panamanian Embassy ran a red light and smashed broadside into another vehicle.

Dr. Halla Brown, a passenger in the other car with her husband, was paralyzed for life from the neck down. She spent 19 months in hospitals at a cost of more than $200,000.

Though police reports indicated the Panamanian driver was in the wrong, he could never be compelled - and never did - pay any damages for the accident.

In another widely noted auto accident, a 19-year-old Virginia highway repairman was killed in Arlington in 1976 when he was struck by a car driven by Senegalese Embassy chauffeur. An Arlington judge later set aside the driver's calim to diplomatic immunity, but only after pointing out that the chauffeur had subsequently been fired by the embassy and that the accident occured inside the scope of his job.

Both these incidents have been cited by Rep. Joseph L. Fisher and Sen. Charles Mac Mathias, the principal proponents of the bill in the House and Senate, as underscoring the need for legislative curbs on diplomatic immunity laws.

Another less serious but nonetheless annoying aspect of diplomatic immunity is the protection the laws offer from even minor traffic regulations.

Tens of thousand of parking tickets are ignored every year by employes of numerous embassies and diplomatic missions here. The Russian, Israeli and Peruvian embassies usually head the list of scofflaws.

The D.C. City Council recently approved legislation to "decriminalize" parking ticket cases by transferring them from the court to a board of civilian hearing examiners. The changeover is expected to occur this fall although jurisdiction over more serious traffic violations will remain in D.C. Superior Court.

The new parking ticket enforcement system would put increased pressure on diplomatic employes without civil immunity to obey the city's parking regulations. And, if Congress does restrict diplomatic immunity for lower-echelon embassy employes, officials say thousands of them could be required to pay their accumulated parking fines.