Riding the Reagan landslide, Republicans yesterday knocked off House Majority Whip John Brademas (D-Ind.) and made their hardest run at House Democrats since 1966.

It appeared that Republicans would easily exceed the 20-seat pickup predicted for them as the campaign closed. As counting moved west, it appeared the GOP might gain 30 or more seats, which would be its best record since it rebounded from the landslide losses of 1964. That would still be short of the 59 seats Republicans need to win back control of the House for the first time in a quarter-century. But if Republicans hold the early gains, it means a considerably more conservative House next year.

Majority Leader Jim Wright (D-Tex.), thought by some to be in a close race, won easily as did Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.).

But some other senior Democrats appeared to be following Brademas, the third-ranking Democratic leader, to defeat. Rep. Thomas L. Asley (D-Ohio), chairman of the House housing subcomittee and a 26-year House member, lost. Rep. Frank Thomas (D-N.J.), another 26-year veteran and the House Democrats' labor expert, went down to defeat, apparently because of indictment on Abscam bribery charges. On the West Coast, House Ways and Means Chairman Al Ullman (D-Ore.) also was trailing narrowly with nearly half the vote counted in his race for a 13th term.

Rep. Bob Eckhardt (D-Tex.), liberal opponent of big oil, was behind in Houston by two percentage points with more than 90 percent of the vote counted. Agriculture Chairman Thomas Foley (D-Wash.) was leading 52 to 48 in a close race.

In the Midwest, Rep. Samuel Devine (R-Ohio) third-ranking member of the GOP House leadership as conference chairman and a 22-year member, was beaten in Columbus by attorney Bob Shamansky whom Devine defeated 14 years ago. But in Wisconsin, Democrat Robert Kastenmeier, also an 11-term verteran thought to be in trouble, won reelection.

Also beaten was Rep. John Murphy (D-N.Y.), 20-year House member and chairman of the Merchant Marine Committee until he too was indicted in the Abscam case. In South Carolina, Rep. John Jenrette (D), convicted on Abscam charges, was defeated. In Philadelphia, Michael Myers, expelled from the House after his Abscam conviction, lost a reelection bid to an independent who will vote with the Democrats.

But several Democrats believed to have good to fighting chances to win were also defeated or losing. In Rhode Island, Rep. Edward Beard (D), a former house painter, was defeated by a former TV talk show host.

Perhaps for ethnic reasons, Democrats lost the New Haven seat retiring Rep. Robert Giaimo had held for 22 years. The winning Republican had an Italian name. The Democratic nominee was Jewish.

Democrats lost three of their four remaining seats in Virginia. The two northern Virginia liberals -- Herbert Harris and Joseph Fisher -- were defeated and the Richmond seat went Republican after the retirement of conservative Democrat David Satterfield.

In North Carolina, Democratic Rep. Richardson Preyer, "Mr. Integrity" of the House, was trailing with incomplete returns. In New Jersey, Rep. Andrew Maguire (D), who won a Republican seat in 1974 and had held it closely since, was defeated. Democrats lost the swing seat in Omaha when two-term Democrat John Cavanaugh retired after two terms.

Rep. Robert Bauman (R-Md.) was defeated, but the other incumbent Republican with ties to the homosexual community, Jon Hinson of Mississippi, won reelection.

Brademas lost to John Hiler, a conservative 27-year-old businessman. The South Bend representative had usually won in close races. This time unemployment, a growing disenchantment with government, and perhaps a tendency to blame leaders more than other elected officials for the nation's problems caught up with him. Democratic campaign officials had carried him at the top of their endangered list for some time.

Several leading Democrats in the west were believed in close races. Rep. Morris K. Udall (D-Ariz.), Interior Committee chairman, was ahead nearly 2 to 1 with 20 percent of the vote counted. Public Works Chairman Harold (Bizz) Johnson (D-Calif.) was trailing.

There will be at least two additions to the 14-member all-Democratic Black Caucus in the House. The solidly Democratic Chicago district from which Morgan Murphy retired nominated a black -- Chicago's third -- to replace him while, in Los Angeles, Mervyn Dymally, former lieutenant govenor, was also considered a shoo-in.

An increase in the group of 16 women now serving in the House also was assured. Fifty-one were running as major party candidates. One incumbent woman, Elizabeth Holtzman (D-N.Y.), left to run for the Senate. But Republicans have a sure replacement in the safe Illinois district John Anderson gave up to run for president.

Fifty-one candidates had no major party opposition and could be presumed elected before the polls opened yesterday morning.

As usual, most members of the remarkable Democratic class of 1974 were under pressure in close races. Seventy-five Democrats, many of them with no previous political experience, were first elected in 1974 after Watergate. Usually, after such a landslide has wrenched many seats away from the party that long held them, the pendulum swings back in the following election to return most to their original party.

That happened in 1966. Two years earlier, during Lyndon Johnson's landslide presidential victory over Barry Goldwater, Democrats picked up 37 House seats that were traditionally Republican. But in 1966 Republicans came back to pick up 47 seats held by Democrats.

But that did not happen to the Watergate class. Not only was there no big bounceback in 1976, but also Democrats gained a seat in the House. Two years ago Republicans gained 15 seats in the House. But only seven of those 75 Democrats first elected in 1974 have been defeated, and 56 are still serving.

Several of them are usually placed on the endangered list early in each campaign -- such as Maguire of New Jersey, Robert Edgar of suburban Philadelphia and Timothy Wirth of Colorado.But each has survived two cliffhanging reelection campaigns and may again.

There were 43 open House seats to be filled yesterday -- ones where the incumbent was not running. Democrats conceded three before the polls opened, in Virginia, New York and Missouri, believing only the retiring incumbent's conservative or other personal appeal could hold the seat in the Democratic column. Most observers were willing to concede two open Republican seats to the Democrats, in North Dakota and California.

Some House turnovers, if they occurred, could be attributed to unique problems of the incumbent. Two Republicans were burdened by ties to the homosexual community. Some Democrats had been indicted, and two of them convicted, if bribery charges stemming from the Abscam operation. Some senior Democrats, including such committee chairmen as Al Ullman (Ore.) of Ways and Means, Morris K. Udall (Ariz.) of Interior and Tom Foley (Wash.) of Agriculture, were said to be in some trouble because they spent too much time on their Washington duties and had grown out of touch with their districts. But they were expected to survive.

Of the Republicans expected to be returned to the 97th Congress that will convene in January only Minority Leader John Rhodes (Ariz.) and William Wampler (Va.) have ever served in a Republican House. That was 1953-55 when both were first-termers. Rhodes, for one, has had enough of serving in the minority. He said he would like to be Speaker, but if that is not to be he will serve one more term as just another member and then retire. Already running to succeed Rhodes are Robert Michel (Ill.), now the whip, and Guy Vander Jagt (Mich.), chairman of the House GOP campaign committee.