The largest, costliest union organizing effort of the 1980s is under way here, with a dozen unions spending more than $10 million in an election campaign that is a proving ground for labor's effort to reverse its decline by attracting a new breed of union member.

Using techniques that have proved effective in national political campaigns -- from slick television ads and opinion polling to computer-targeted direct mail and satellite-fed news conferences -- unions are scrambling to sign up the younger, predominantly female legions of office workers and service employes who make up the fastest-growing sectors of the nation's work force.

The target of the effort here is 50,000 Ohio state government employes and up to 500,000 more municipal, county and school board employes who are eligible to unionize because of a collective-bargaining law that took effect last year.

The intensity of the campaign -- which has attracted 91 percent voter turnout in 200 local elections so far -- reflects the desperation of unions for new membership, and also is a gauge of how interested many public-sector workers are in union representation.

Nationwide, private-sector union membership has declined to 19 percent of the work force. But public-sector representation has steadily increased to 35 percent -- and is growing, according to Labor Department data.

Here, unions have won 68 percent of the elections, but the "no-union" votes in 45 elections have been higher than expected, state and union officials say, partly because some local governments have spent substantial sums hiring antiunion labor-consulting firms. The results of the biggest mail-ballot election among 10,000 state workers will be announced next week.

"In terms of attitudes about unions, Ohio has everything. You've got the northeastern, heavily industrialized towns like Cleveland and Youngstown, where unions have a history, and it's prounion. But you've got those southern attitudes down around Cincinnati, where it turns rural . . . and we don't do too well," said John Toto, a New York union official here to direct the campaign of the American Federation of State, County and Municipal Employees (AFSCME).

The key voters here are the same bloc courted by Democratic and Republican strategists: Neither blue-collar nor white-collar, they are the $15,000- to $25,000-a-year clerical and technical workers with new-sounding job titles such as technical typist, clerical specialist or programming aide.

Their primary work place complaint is usually low wages, which in Ohio average about $18,000 a year, roughly 10 percent below the national average for public employes. But these government workers also have deep concerns about job security, stress, pay equity between male and female workers, career advancement, and having a voice in decision-making.

Like their job titles, their attitudes about unions and politics may also be quite different from those of their parents. Unions are discovering this difference as they meet a range of responses from strong support to indifference and hostility. AFSCME said its polling among Ohio state workers indicated support for unionization ranging from 80 percent among blue-collar workers to about 50 percent among professionals.

"Educating people about unions is our biggest task," said Toto, a former New York City sewage plant worker who rose through AFSCME ranks. "Many people don't understand what collective bargaining is . . . . They thought when April 1 came the date the new law took effect they would get an automatic pay raise. But now they realize there's a lot more involved."

For Ardyth Dempsey, a 45-year-old technical typist at the Ohio Department of Human Services, a labor union is a long-overdue protection against what she sees as abuse by "the state system." After seven years, she earned $6.63 an hour for a job that involved primarily typing and filing. But Dempsey said that additional duties were steadily tacked onto her job, such as handling payroll, auditing travel vouchers, scheduling appointments for her boss, and supervising two other typists. "I'd also get other bosses coming in here and assigning me work, beyond my own boss' work," she said.

Dempsey said she learned of a "job audit" process through AFSCME literature. She demanded that her job be reviewed, and last month she won a $1-an-hour pay raise and the new title of secretary.

"That's why I think a union would be good," she said, " . . . I'm not certain what a union will do, but it's someone to go to and say 'Hey, if I do this, what will happen to me? . . . . What can I do?"

Others, however, have had bad experiences with unions. Susan Bankston, 32, a telephone operator, joined AFSCME even before the new bargaining law. But when she nearly lost her job for taking an unauthorized absence, she said, "I called AFSCME and they weren't ready to help me. I had to make an appointment to see them and they weren't much help."

Bankston said she now supports a competing union, the 650,000-member Communications Workers of America. CWA, the longtime telephone-company union, represents about 80,000 public employes in New Jersey, Texas and other states and is making a major push against AFSCME, portraying the bigger union as top-heavy, unresponsive and less aggressive.

Other unions vying for state and local employes include the International Brotherhood of Teamsters, the National Education Association, the Fraternal Order of Police, the Service Employees International Union, the United Steelworkers of America and a coalition of building trades including the Carpenters, Operating Engineers, Plumbers and Painters.

AFSCME is a favorite target of other unions because it is outspending all of them combined, by most estimates. While other unions are passing out leaflets, AFSCME is bouncing TV signals off a satellite from its Northwest Washington headquarters to Ohio stations, sending out radio news releases and running up a tab of more than $6 million with nearly 100 campaign staffers.

Despite being outspent by perhaps 10 to 1, CWA has won at least four elections against AFSCME, using less media and more personal one-to-one contact between workers and organizers.

"TV ads create excitement, but our people create their own energy. People are very excited . . . about the idea of having more control over their working lives," said Toni Dymek, 35, a former Bell system operator who works for CWA.

By next year, the 1.1-million-member AFSCME expects to win at least 30,000 new members, becoming the largest union in Ohio at more than 100,000 and surpassing the fading Steelworkers, Teamsters, and Rubber Workers. Such a shift vividly reflects the growth of the service sector and the decline of industrial unionism.

AFL-CIO unions are expending considerable time, energy and money attacking each other. "It's a real mess out there," said federation spokesman Murray Seeger. "It should have been a coordinated campaign, but we have too many different affiliates competing." AFL-CIO President Lane Kirkland was forced to order one union, the National Union of Hospital and Health Care Employees, Local 1199, to stop "raiding" Ohio's mental health workers, who already belong to AFSCME.

"We have so many unions in Ohio now because they're having a real difficult time everywhere else," especially because antiunion consulting firms are used in more than half of private-sector union drives, said Charles McDonald, the AFL-CIO's director of organizing.

In Cincinnati's Hamilton County, the government ran a "full-fledged, all-out blood-in-the-streets antiunion campaign," said AFSCME's Toto. The county government, with the help of a consultant, put out antiunion literature and held employe meetings to discuss the drawbacks of voting union, he said. The result: a "no-union" vote by a one-vote margin among 1,000 mental health workers, an outcome that AFSCME is protesting to the new State Employment Relations Board.

"There is nothing wrong with wanting a nonunion atmosphere. But we did not run an antiunion campaign. We just pointed out the facts," said C. Spencer Barkley, the deputy county administrator. The county has spent about $300,000 hiring Clemans Nelson & Associates, a Columbus labor-consulting firm that has been hired by more than 60 counties.

"We pointed out our benefits, our retirement system and hospitalization plans . . . and we depicted some of the strife and problems and conflicts that have gone on with unions elsewhere," Barkley said.

"We are not antiunion. Anytime you put out the employer's side, you get accused of doing something un-American," said Ted Clemans, a former AFSCME official who heads the state's largest labor-consulting firm. He said the firm's primary message during union drives is that with the election of a bargaining agent, employes lose their right to deal directly with management.

Most governments have taken a neutral stance, but many are fighting -- and challenging the new law in court -- because they are facing a financial squeeze, said Raymond Sawyer, chief of staff to Democratic Gov. Richard F. Celeste. Celeste, who has received more than $300,000 in union campaign donations, signed the collective-bargaining law that his predecessor, Republican governor James A. Rhodes, had twice vetoed.

With Rhodes a potential challenger in the 1986 elections, Celeste's opening the door to unions is likely to become a campaign issue, political observers say, depending largely on the size of pay raises that unions negotiate. The state has budgeted $40 million for raises for two years, which unions already said is inadequate.