The Republicans picked up 15 seats in the House of Representatives in Tuesday's elections, with the outcome of three more races, including that of convicted Rep. George Hansen (R-Idaho), still up in the air.

Democratic leaders mostly escaped unscathed. House Budget Committee Chairman James R. Jones (D-Okla.), who faced his toughest reelection ever, won handily. But several other prominent Democrats were defeated, including three subcommittee chairmen, Reps. Clarence D. Long (D-Md.), Elliott H. Levitas (D-Ga.) and Donald J. Albosta (D-Mich.).

Democratic casualties were highest in the suburbs and in the Sun Belt states of Texas and North Carolina, where President Reagan was extremely strong and Republican Senate candidates also won.

Four Texas Democrats, including Rep. Jack Hightower, one of the conservative "Boll Weevil" Democrats, were knocked off and three Democrats lost in North Carolina, including veteran Rep. Ike Andrews.

Republicans, who just days before the election were predicting that a tidal wave for President Reagan would wash two dozen or more House seats into the GOP column, said the gains probably were not enough to change the basic equation of Democratic dominance in the House. Democrats had a 99-seat majority in the 98th Congress that just adjourned.

House Minority Leader Robert H. Michel (R-Ill.) said, "I don't think people should expect too many victories when we are still that number behind."

Democratic Congressional Campaign Committee Chairman Tony Coelho (D-Calif.) said, "There is no question that the House remains in firm working control of the Democratic Party."

Coelho said that, with the exception of North Carolina and Texas, the Reagan landslide had surprisingly little impact on most House races -- unlike 1980, when Republicans picked up 33 seats.

Presidents generally have had little success extending their coattails in winning election to a second term. President Dwight D. Eisenhower lost two GOP House seats in 1956 and President Richard M. Nixon gained only 12 in his 1972 landslide victory.

Democratic leaders said they expected only a slightly more conservative House, because many of the seats picked up by the Republicans came at the expense of conservative Democrats.

Coelho said that, of the Democratic seats given up to the GOP, eight had been in the president's camp anyway. That group included Hightower, two of his Texas colleagues, freshman Rep. Tommy J. Vandergriff and Rep. William N. Patman, Levitas of Georgia and the open Democratic seat formerly held by Rep. Kent R. Hance (D-Tex.).

Democrats picked up three conservative Republican seats, but it was unclear what effect that will have on the ideological balance in the House. Flamboyant Pulaski County Sheriff Tommy Robinson, a conservative Democrat, will take over the Arkansas seat being vacated by conservative Republican Ed Bethune and is expected to vote frequently with Reagan.

Another sheriff, James A. Traficant Jr., who defeated maverick Ohio Republican Rep. Lyle Williams, also was viewed by Democrats as a likely supporter of many administration initiatives. Traficant, who successfully defended himself in court against charges that he accepted bribes when campaigning for sheriff, is expected to be a colorful member of the next Congress.

In southeast Illinois, Democratic state Sen. Terry L. Bruce defeated Rep. Daniel B. Crane (R-Ill.), who was censured by the House in the last session for having had sex with a female page in 1980, and who subsequently apologized to his district. Bruce, while generally conservative in outlook, also has strong labor union ties, which Democrats say will mean a frequent vote in their column.

Rep. Gerry E. Studds (D-Mass.) had more luck in his Cape Cod race. Studds, who was censured for having an affair with a male page, won easy reelection.

Several races were unresolved late yesterday.

In Idaho, Hansen, convicted in April for filing false financial disclosure statements, was trailing Democrat Richard Stallings by 67 votes, but some ballots were being contested. In southwest Indiana, freshman Democrat Frank McCloskey was trailing Republican Richard D. McIntyre by fewer than 200 votes and a recount was in progress.

In the contest for a Salt Lake City open seat formerly held by a Republican, Democrat Frances Farley, an anti-MX missile, pro-ERA activist, was trailing Republican Lt. Gov. David S. Monson by fewer than 150 votes, but more than 2,000 absentee ballots had not been counted.

The new Congress also will include 19 blacks, one fewer than the previous roster. Freshman Rep. Katie Hall (D-Ind.) was defeated in a primary and will be succeeded by Peter J. Visclosky, a former Capitol Hill aide who is white.

In a race that attracted national attention as a test of blacks' voting strength, Democratic state Rep. Robert G. Clark failed for the second election in a row to unseat Rep. William W. Franklin (R-Miss.) and become the first black to represent Mississippi in the House since Reconstruction.

Recent redistricting had made the district 53 percent black, but Franklin, aided by a large white turnout in a highly polarized contest, scored a comfortable victory.

Hispanics increased their numbers in Congress from nine to 10. In San Antonio, retired county judge Albert G. Bustamante won without opposition after defeating veteran Rep. Abraham Kazen Jr. (D-Tex.) in the Democratic primary by emphasizing the need for greater Hispanic representation in Congress.

Women, who lost two of their 22 seats -- Hall's in Gary, Ind., and Democratic Rep. Geraldine A. Ferraro's in Queens, N.Y. -- going into the election, came out even after it. They picked up two seats, and possibly a third -- the open Utah seat.

Helen Delich Bentley, a Reagan supporter, defeated Long in the Baltimore suburbs on her third try for the seat.

Kansas state Sen. Jan Meyers (R) took an open seat formerly held by veteran Larry Winn Jr. (R-Kan.), who retired. Meyers is expected to split with the president more often than Winn. Endorsed by feminist and teacher groups, she favors increased spending on education and the elderly but also supports a balanced-budget constitutional amendment and the MX missile.

Most incumbents with more than one term in Congress won reelection handily Tuesday.

A few who did not were Rep. Joseph G. Minish (D-N.J.), an 11-term incumbent whose northern New Jersey district was redrawn to make it more Republican; Rep. William R. Ratchford (D-Conn.), who survived a close call in the Reagan sweep of the 1980; and Rep. Jerry M. Patterson (D-Calif.), elected 10 years ago in the Democratic surge during the Watergate scandal.

Patterson was defeated by former representative Robert K. Dornan, who ran unsuccessfully for the Senate in 1982 and moved into Patterson's Orange County district a few months before the election. Although Patterson often walked a carefully moderate line in the House, Dornan painted him as too liberal for the conservative district.

Several other incumbents won by narrow margins. Two other "Watergate babies," Reps. Robert W. Edgar (D-Pa.) and Philip R. Sharp (D-Ind.) won, but in Edgar's case, a recount has been ordered. Rep. Robert A. Young (D-Mo.), in the St. Louis suburbs, also was reelected after a tough fight.

Depending on the outcome of a few tossup races, 42 to 44 new members will be sworn into the 99th Congress. The number is unusually small, largely because of the small number of retirements. Eighty-five freshmen were elected to the 98th Congress.

Sixty-one of those freshmen were Democrats elected in the depths of the 1982 recession. Those seats became a key battleground in this election, as the GOP targeted many of the Democratic first-termers.

In Tuscon, Rep. James F. McNulty Jr. (D-Ariz.) was defeated in a rematch with former state senator Jim Kolbe. McNulty had squeaked by to win election in 1982 in a conservative district that strongly supported Reagan.

In North Carolina, two Democratic freshmen were buried by a Reagan avalanche. Rep. Robin Britt of Greensboro and James McC. Clarke of North Carolina's rural western region lost, in both cases to Republicans who had firmly grabbed Reagan's coattails. Britt and Clarke generally voted with the House Democratic leadership.

In the Fort Worth suburbs, Vandergriff also sank under a strong Republican tide. While he has voted with the president more than with his party leadership in the House on most of Reagan's initiatives, his opponent, economics professor Richard Armey, cast Vandergriff as a free-spending liberal.