The Virginia Senate, over the objections of lawmakers who had helped stall the racially charged issue for seven years, today approved making Martin Luther King's birthday a state holiday.

If approved by Gov. John N. Dalton, Virginia will become one of just three states along with the District of Columbia to so honor the slain civil rights leader.

The bill was one of dozens of measures passed by both houses on the eve of the legislature's scheduled adjournment from a 38-day session that has been marked by flights over tax relief and spending a $201 million surplus.

Today the legislators also approved bills adding multiple murders to the list of crimes punishable by death, removing a requirement that Washington's Metro system submit wage proposals to binding arbitration, restricting strip-searchers of prisoners by jailers, and allowing citizens to sue the state of Virginia in certain accident cases.

The Jan. 15 holiday for King was approved 24 to 13 at the urging of L. Douglas Wilder of Richmond, the Senate's only black member who portrayed the bill as a test of the state's commitment to racial equality.

"It's become a focus for black aspirations in this state and a measure of just how genuine the legislature's concern for those aspirations is," said Wilder, noting that King now joins Confederate generals Robert E. Lee and Stonewall Jackson, who are honored by a Virginia holiday.

Some of the bill's opponents objected to setting aside a special day for a non-Virginian and others were unhappy that the measure scrapped Election Day as a holiday in order to avoid giving state employes another day off each year.

The death penalty bill had died in a House committee last year but this year was approved 67 to 27, despite warnings from opponents that the bill was unconstitutionally vague and unenforceable. Supporters said the bill, sponsored by Fairfax Sen. Richard Saslaw, filled a gap in the present statute and assured that mass murderers would face the same punishment that those guilty of several other types of murders face.

Saslaw also sponsored the bill tightening the state law governing strip-searchers, which passed the House 73 to 17. The measure was inspired by incidents at the Arlington County Jail involving persons accused of minor infractions.

The Metro measure, proposed by Northern Virginians as a way to hold the lid on rapidly escalating transportation costs, passed by 71 to 15 despite opposition from organized labor. It will have to be passed by Congress and by Maryland and the District of Columbia before it can become effective under the compact that governs the transit system.

Fairfax Del. Warren Barry argued the wage increases triggered by the arbitration requirement put an unfair burden on Northern Virginians who underwrite Merto operating costs through their real estate taxes. Barry said the average Metro driver earns about $22,400 annually and has seen his salary rise by 84 percent since 1974, compared to a 49 percent increase for other area workers.

But opponents said arbitration was the only fair way to deal with labor disputes and to avoid plunging the state into a series of public employe strikes. "This bill is a literal time bomb that could cause labor problems such as have never been experienced in the commonwealth," argued Del. Lewis P. Fickett of Fredericksburg, a labor law professor.

The House reversed itself today on Alexandria Sen. Wiley F. Mitchell's bill removing the state's sovereign immunity in negligence cases. The bill, which limits the amounts citizens can recover from the state to $25,000 in most cases, failed yesterday on a close vote but passed today after a night of intensive lobbying.