The Senate agreed last night to drop about half the extraneous legislation that senators tried to tuck away in the huge budget-slashing bill that the Senate is expected to approve this week.

The voice vote, with only a handful of senators present, ratified an agreement negotiated earlier in the day by Republican and Democratic leaders to meet objecctions raised by Sen. Ernest F. Hollings (S.C.) and other Democrats on the Budget Committee.

Acknowledging that the bill making nearly $40 billion in cuts had been padded with non-budgetary changes in law, the leaders agreed to strip out provisions to do such things as permit wider trucks on interestate highways, deregulate the amateur radio industry, allow Western Union to enter international telecommunications markets, reauthorize the Older Americans Act and create a new program sponsored by Sen. Jeremiah Denton (R-Ala.) to promote adolescent chastity, sources said.

But they disagreed over other items in such areas as further radio deregulation, television licensing, federal controls over community development grants and curtailment of subsidized housing assistance for cities like Washington that practice rent control. These issues will have to be fought out on the Senate floor or in a House-Senate conference.

"People saw the train pulling out of the station and they just all got on," said Majority Leader Howard H. Baker Jr. (R-Tenn.) in acceding to Democratic claims that the so-called budget reconciliation measure had been "loaded" with excess legislative baggage because it provides a shortcut to enactment.

Under special provisions for approving spending cuts proposed by committees under the reconciliation process, filibusters are banned and other restraints are imposed on a minority's power to delay and obstruct. Hence the Democrats protested. Baker said he agreed that overloading of the reconciliation bill could set a dangerous precedent, although the Republicans refused to go all the way in stripping it down, partly to keep some bargaining leverage when the measure goes to conference with the Democratic-controlled House.

Meanwhile, Senate Democrats came up with another proposal, which would add back more than $1 billion to the $39.6 billion in spending cuts, mostly to keep the Social Security minimum benefit. Baker said he was reserving judgment on the Democratic proposals but would oppose any net loss in savings.

The Democrats would add back $925 million to keep the Social Security minimum benefit for current recipients only, $80 million for foster care and adoption, $45 million for summer feeding for children, $40 million to keep the Economic Development Administration operating at 40 percent of its current level instead of closing down and $30 million to shield the elderly and disabled from proposed food stamps cuts. They would also add $69 million in 1984 to block plans to stop funding school lunches in orphanages and institutions for the retarded in that year.

Senate Democrats, who were beaten in earlier attempts to modify President Reagan's proposed budget cuts, acknowledged that their latest proposals were modest. They are basically to "plug holes in the safety net" that Reagan promised to maintain for needy Americans, said Minority Leaders Robert C. Byrd (D-W.Va.).

Senate approval of the legislation is expected by week's end, although it is unclear whether action on the measure can be finished before Congress' July 4 recess in the House, where the Reagan administration and the Democratic leadership are locked in a fight over what cuts to approve.