In a small romm on the third floor of the Indiana State Teachers Association Building here, the Republican Party took a first step last month toward one of its most cherished but elusive goals -- control of the U.S. House of Representatives.

The room, which is tucked into a corner of state Republican Party headquarters, has only one distinguishing feature -- a compueter terminal. For three weeks last month, two men worked night and day in the small room, peering at the numbers on the terminal screen as they refashioned Indiana's political boundaries. When they were finished, one of the men, Allan Sutherlin, pronounced himself satisfied.

"The party out of power learned a tough lesson in Indiana this year," he said of the congressional redistricting plan signed into law recently by Republican Gov. Robert D. Orr. "This is a gotcha plan. . . . This map will defeat three incumbent Democratic congressmen."

Sutherlin's prediction will not be tested until the 1982 congressional elections, by which time any number of factors could upset his plan. Certainly the three Democrats who have been targeted for extinction -- Floyd J. Fithian of Lafayette, Philip R. Sharp of Muncie and David W. Evans of suburban Indianapolis -- have shown no sign they are ready to give up without a fight. But even the Democrats here concede that the newly drawn congressional district lines are a political masterpiece and that they face a much tougher task now in retaining their one-vote majority in Indiana's congressional delegation.

Indiana is one of the first states in the country to complete its congressional redistricting. In the next year or so, other states will do the same, redrawing congressional district lines to reflect shifts in population as measured by the 1980 census. In the process, individual political careers will be made and broken and -- Republican officials on both the state and national levels hope -- the GOP will complete the takeover of the federal government it began in the election of 1980.

The Republicans control the White House and have a majority in the Senate; the Democrats have a 26-vote majority in the House. Republican officials such as national committee chairman Richard Richards believe the House, too, can be theirs after the 1982 elections, provided President Reagan remains popular and provided that the GOP is treated fairly by state legislatures in the redistricting process.

In Indiana, the Republicans treated themselves more than fairly.

John Livengood, executive assistant to Indiana Democratic chairman Donald Michael, reflected one day last week on the redistricting process as he saw it.

"Certainly, we expected the maps to have a Republican flavor," he said. "After all, they drew them. But we didn't expect them to go for the jugular. "We didn't expect them to try to do away with the Democratic Party."

The Republicans could "go for the jugular" here because of several factors. While nationally the Democrats have control of a majority of state legislatures, the GOP, with the governor's office and majorities in both chambers of the Indiana General Assembly, had firm political control of the redistricting process through the legislature in one day at the end of the regular legislative session.

Like their fellow Republicans on the national level, Indiana Republicans have no money problems these days. They spent an estimated $250,000 redrawing the congressional and state legislative districts this year, more money than the entire yearly budget of the state Democratic Party.

Most went to buy highly sophisticated computer technology from Market Opinion Research, the Detroit-based firm headed by Robert Teeter, one of the most repected Republican pollsters in the country.Here again, the Indiana GOP reflected what Republicans will be doing across the country in the months ahead -- using the latest in technology to take advantage of situations where the enjoy political control, and to counter the Democrats in those states where the Democrats control the redistricting process.

Democrats, lacking the funds to buy the services of firms like MOR, are currently downplaying the importance of computer technology in politics.

"At its heart, redistricting is a political rather than a technological struggle," said Martin Franks, executive director of the Democratic Congressional Campaign Committee. "The guys that drew that [Indiana] map knew what they wanted to do before Bob Teeter and his computer came in."

Still, Franks conceded, he and other Democrats might feel differently if they had the money to buy that kind of expertise. "Once you've made the political decision on who you want to screw, it helps to have a nice map to make it all stand up in court."

Allen Sutherlin could not agree more. Only 31, a biologist by training, he has spent the last nine years in political work, most recently as secretary and political director of the Indiana Republican Party. In February he left the party post and, with a partner, formed a consulting firm that served as the link between the Indiana GOP and the Teeter firm for the redistricting process.

Sutherlin and other Indiana Republicans knew what they wanted to do. They knew, for example, Sutherlin said, that at all costs they must keep the city of Anderson, site of the nation's largest United Automobile Workers union local, in a different congressional district from the nearby city of Muncie, site of another large UAW local. Combined, those two cities would form a powerful base for a Democrat, possibly providing a springboard to statewide office for the right candidate. Separated, they would be relatively harmless to the Republican cause.

MOR's computers were not necessary to tell the Republicans that. But crammed with information about Indiana, its people and its politics, they could tell Sutherlin and his cohorts other things. By hitting a few keys on the terminal, Sutherlin could summon any of 92 separate items of information on some 2,900 precincts and other subdistricts in the state.

Some contained basic data from the Census Bureau -- the population of a precinct and its racial makeup. Most of the items contain political information -- the voting habits of those people.

For three weeks Sutherlin and Fred Steeper, vice president of MOR, worked in the small room, negotiating the necessary political compromises with the state legislators and members of the congressional delegation, using the computer to track exactly what would be the makeup of the new districts they were fashioning. In the end, the plan they produced had these features:

The congressional district currently represented by Fithian no longer exists. Because its population growth lagged behind southern and western states, Indiana's congressional delegation will be reduced from 11 to 10 members in the 1982 election. The counties that now make up the 2nd Congressional District have been scattered into four other districts. Fithian's home in Tippecanoe County has been moved into the congressional district represented by Republican John T. Meyers. Fithian calls this "an abomination." Sutherlin, smiling slightly, says Fithian will face "a very challenging situation" in 1982.

The homes of three incumbent Democrats -- Evans, Sharp and Lee H. Hamilton -- are all located in the new, heavily Republican 2nd district. Hamilton can solve his problem easily by moving a few miles south, back into the 9th Congressional District he now represents. But Evans and Sharp face much more difficult options, which include running against one another, running separately in districts that have been stacked for the Republicans, or running against popular Republican U.S. Sen. Richard G. Lugar.

Two districts represented by Democrats -- Hamilton's 9th district along the Ohio River and the industrial 1st Congressional District represented by Adam Benjamin Jr. -- have been made more Democratic. This was not a case of Republican soft-heartedness, but a calculated decision to all but concede some districts to the Democrats to improve GOP chances elsewhere in the state. Thus, normally Democratic Michigan City was placed in Benjamin's district, removing it from the 3rd Congressional District, which the Republicans captured from John Brademas in 1980 and would like to retain in 1982.

Anderson is an isolated Democratic pocket in the new 6th Congressional District, a heavily Republican area that just happens to contain the home of Bruce Melchert, the state Republican Party chairman.

Muncie is an isolated Democratic area in the new 2nd district, which should be another GOP stronghold and which happens to contain the home of Republican state Sen. Charles E. Bosma, chairman of the Senate committee that handled the redistricting legislation.

The map isn't perfect from a Republican standpoint, but it will do, Sutherlin said. Other things begin equal, it should transform what is now a 6-to-5 Democratic majority in the congressional delegation into a 7-to-3 Republican majority.

The Democrats, of course, are screaming. But they are uncertain as to whether they want to undertake the expense of challenging the plan in court because they can't be certain of winning.

"What is immoral may not be illegal," Livengood said.

The Democrats are counting on a voter backlash on the issue to help them in 1982. But they concede this first skirmish in the long battle over redistricting the House to the Republicans. There are few places in the country where the GOP will enjoy all of the advantages that they did here, but if the Republicans are finally going to seize control of the House they are going to have to get the most from those places where they hold the edge.

Much more than the Congress elected in 1982 will be affected. The lines drawn this year and next in Indiana and the other states will remain in effect until after the 1990 census, and the candidates elected within those new lines will reap the benefits of incumbency. Four of Indiana's six Democratic congressmen, for example, were first elected in 1974, the year of the Democrats' "Watergate landslide," and have been able to beat back Republican challenges since then. Should three of them be dislodged in 1982, it would be their GOB replacements who would become the entrenched incumbents.

For these and other reasons, Sutherlin said, the $250,000 the Indiana Republican Party spent on the redistricting program was a cheap investment that will pay dividends the rest of the decade.

"We definitely got our money's worth," he said. "In terms of the long-term gain to the Republican Party of Indiana, the system would have been a bargain at twice the price."