Proponents of a freeze on nuclear arms were jubilant yesterday, calling their eight-state victory at the polls "a clear and unprecedented mandate" to the Reagan administration to open freeze talks with the Soviet Union. They predicted that an additional push will come soon from the new Congress, but the White House was not impressed.

Nearly 18 million people voted on the issue nationwide, splitting 10.8 million in favor and 7.2 million opposed, according to freeze advocates. It was the most common among more than 60 ballot questions in 24 states.

In one of the most significant votes, a stiff gun control measure was defeated in California after a vicious, high-spending battle. Nuclear power plants were all but prohibited in Massachusetts, although Idaho and Maine voters endorsed them strongly.

Alaska voters refused to cut off state funding for abortion and denied money for transfer of the state capital out of Juneau, and Massachusetts decided to restore the death penalty, while four out of five states rejected returnable bottle bills.

"The momentum is here for a nuclear freeze movement in the 1983 Congress and in the 1984 elections," said John Isaacs of the Council for a Livable World, which claimed to have given significant help to winners of 11 Senate and 32 House races. He said voters had delivered "a clear and unprecedented mandate" that "the nuclear arms race must be stopped once and for all."

The nonbinding freeze proposals lost in Arizona and passed narrowly in California following a barrage of "anti-freeze" speeches and letters from Reagan administration officials and conservative groups. They passed decisively in Massachusetts, Michigan, Montana, New Jersey, North Dakota, Oregon, Rhode Island and the District of Columbia.

Additional support came from ballots cast in 26 of 29 cities and counties, including the Miami, Chicago, Reno, Philadelphia and New Haven areas.

White House spokesman Larry Speakes, recognizing the votes as "an expression of concern and a desire to achieve progress on arms control," said President Reagan "would like to see a freeze, too, but only after major reductions to equal, verifiable levels have been achieved."

In related but contradictory decisions, Colorado defeated, 2 to 1, a move to fund conversion of the Rocky Flats nuclear weapons production plant to peaceful uses, while voters in Cleveland banned spending of city money on "useless" civil defense efforts against nuclear attack.

Majorities in several states made clear their opposition to control of guns in their own communities.

Californians rejected a proposed handgun registration law by a decisive 2 to 1 ratio. In Sunnyvale, Calif., center of the nation's high-tech semiconductor industry, a proposed ban on sale and possession of handguns trailed.

In New Hampshire and Nevada, more than 70 percent of voters approved state constitutional amendments reaffirming the right of citizens to bear arms.

Jubilant National Rifle Association officials said the results refute polls finding large majorities favoring gun control.

"Votes talk," NRA spokesman Andrew Kendzie said. He acknowledged that a well-financed media campaign had helped defeat the California initiative but added that "the other side had free endorsements from newspapers all over the state."

Howard Gingold of Californians Against Street Crime, which organized the initiative, confirmed that 10 of 11 major California newspapers backed the proposition but said opposition spending easily overcame that.

"This vote demonstrated that there is an atmosphere of fear in California," he said.

The future of nuclear power plants was affirmed in two states. New nuclear plants and waste disposal sites were effectively banned by 2 to 1 in Massachusetts, where such proposals now must negotiate tough legislative roadblocks and pass a citizen referendum.

But Idaho voters decided to require that any restriction on atomic energy be referred to the electorate, and Mainers rejected by 5 to 4 an attempt to ban nuclear power that would have shut down the Maine Yankee plant in Wiscasset. A similar measure failed in 1980, but proponents said they would keep trying.

Some of the biggest bucks were spent on whether to require a five-cent deposit on returnable beverage containers. Citizens in Massachusetts affirmed that their year-old law should take effect, but the proposal was trashed in California, Washington, Arizona and Colorado.

John Gallagher, who headed the "No on Proposition 11" bottle bill opposition group in California, defended the estimated $6 million that container manufacturers, grocers and organized labor spent there. "We make no apology for the kind of money we have raised in order to do this," he said. Opponents in Massachusetts had argued that stockpiled returnable bottles would result in a plague of cockroaches.

As part of a four-state anticrime move, Massachusetts voters restored the death penalty 2 to 1, but the state legislature must decide which crimes will be so punished. Floridians ordered law enforcers to abide by Supreme Court rulings on seizing evidence, which will provide more leeway than under the state's courts. Bail will also be harder to get now in Florida, Colorado and Arizona.

Alaska voters refused 3 to 2 to end state funding for abortion, but decided not to spend $2.8 billion to move the capital from Juneau two time zones west to remote Willow. They affirmed hunting and fishing preferences for native and rural Alaskans and approved 3 to 1 a call for state takeover of federal lands. Arizonans refused 5 to 4 to repeal a similar resolution.

Residents of Battle Creek, Mich., agreed to merge with the surrounding Battle Creek Township after Kellogg Co. threatened to leave if they did not. Another merger between Louisville, Ky., and suburban Jefferson County was so narrowly defeated that there will be a recount.

Gambling expansion lost in Montana and South Dakota, but parimutuel betting got the starting bell in Minnesota while North Dakota will continue to allow gambling for charity. Near Las Vegas, Lincoln County voters defeated, 993 to 595, a proposal to reinstate houses of prostitution abolished there five years ago.

In other novel decisions, "denturists" who are not dentists can install false teeth in Idaho, and electroshock treatments for psychiatric disorders are banned in Berkeley, Calif. Corporations were narrowly barred from owning more farmland in Nebraska, and a high-speed train to connect Ohio cities was killed as a tax nightmare.

Portland, Ore., and two Vermont towns called for an end to U.S. military aid to El Salvador, and Washington state rejected a proposed 12 percent ceiling on interest after banks threatened to leave the state if it passed. San Francisco voters decided not to spend $700,000 to study a possible city takeover of Pacific Gas & Electric Co. operations there.

District of Columbia voters approved a proposed constitution for New Columbia, the next step to becoming the 51st state.