The 98th Congress opened yesterday with festive swearing-in ceremonies, bipartisan calls for swift action on unemployment and Social Security and moves by the House leadership to increase its control over backdoor bills and wayward Democrats.

In the most dramatic show of their party's determination to reassert control of the House, the Democrats' Steering and Policy Committee voted 26 to 4 to remove Rep. Phil Gramm (D-Tex.) from the powerful Budget Committee.

Gramm, who was the most rebellious of the "Boll Weevil" conservative southern Democrats in the 97th Congress, voting with the Republicans more than 90 percent of the time, became the first House member to be stripped of a committee seat for party disloyalty since at least 1911.

Gramm, who has been prepared to switch parties, is expected to resign his congressional seat and run again as a Republican in a special election, sources said last night.

A special election could be held in about three weeks, and the well-funded Gramm would have an edge over any Democrat opposing him. In addition, the strongest potential opponent in the district is a newly elected Democratic state senator who is not likely to give up his position to challenge Gramm at this time.

The advantage of resigning to run in a special election rather than simply switching parties is that, if elected, Gramm would have greater credibility in Congress as a Republican and the election would provide him with the publicity he has been seeking, sources said.

"It's got real drama," one source said.

While the Democratic leadership expressed its displeasure with several other Boll Weevils last session, Gramm is thought likely to be the only one to lose any committee assignments.

Gramm said yesterday he was punished for "practicing in Washington what I preached at home. I'm disappointed. I'm being punished for trying to reduce federal spending and for bringing a balanced-budget amendment to the floor."

The House began the day with Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) telling the new Congress, which features 81 new members and 26 more Democratic votes, that "the American people want action, not partisan bickering."

But the few substantive actions of the new Congress on its first day turned out be partisan and somewhat bitter. On a virtual party-line vote, the House adopted several rules changes that Republicans said were a power grab by O'Neill and the leadership.

The most significant all but prevents the attachment to appropriations bills of so-called riders, which in the past have been used to circumvent everything from the Vietnam war to school busing, wilderness leasing and abortion.

Minority Leader Robert H. Michel (R-Ill.) said this and eight other rules changes would only make it easier for the House to avoid votes on controversial subjects.

"Mr. Speaker, you are taking a body of representatives and turning them into robots, in a glass-covered dome, who come only when they are called, speak only when they are told and cast their votes only when it is unavoidable," said Michel, who only an hour earlier had offered O'Neill an olive branch to symbolize the desire for bipartisanship.

In the Senate, the only action yesterday was the swearing-in by Vice President Bush of 33 members, including five freshmen, who were elected in November.

Majority Leader Howard H. Baker Jr. (R-Tenn.) said his main goals in the new session would be "increasing economic activity, producing jobs, and solving the Social Security problem," which he acknowledged "may be the greatest challenge of the year and the biggest challenge I've ever faced."

In response to the filibuster against the highways-gasoline tax bill that tied up the Senate for much of its lame-duck session last month, Baker said he and Minority Leader Robert C. Byrd (D-W.Va.) would appoint an informal group of senators to consider rules changes limiting debate. Baker also said he would reintroduce his measure to have Senate proceedings televised.

In the House, meanwhile, the Democrats saw to it that the first bill introduced yesterday--which will be HR 1 in this Congress--was the one resubmitting for ratification the Equal Rights Amendment, which died last June after an unsuccessful 10-year effort to win approval of the required three-fourths of the nation's state legislatures.

Rep. Don Edwards (D-Calif.) said his House Judiciary subcommittee on constitutional rights would hold hearings on the ERA early in the new session, and predicted that it would swiftly pass the House, where it has 221 co-sponsors.

"I challenge the Republican-controlled Senate to do likewise," said Edwards. "Only in this way can the Senate show that it is truly committed to women's equality. Symbolic, piecemeal measures simply will not do."

The amendment's fate in the Senate is uncertain. President Reagan has said he supports women's rights, but not the ERA, and support for the admendment was taken out of the Republican Party platform in 1980.

The nuclear freeze resolution also was reintroduced in the House yesterday, with more than 150 co-sponsors.

There was a family atmosphere in the House yesterday, as dozens of young children sat in the chamber next to their fathers and mothers. One young girl brought along her teddy bear, and another stood on a table and applauded as O'Neill was reelected speaker.

O'Neill, frustrated in his efforts to move a jobs bill through the lame-duck session at the end of the last Congress, made it clear that helping the unemployed would be his top priority this year.

"I am confident that the members of this House will get to work putting America back to work," he said. "As this Congress convenes there are 4 million more Americans out of work than two years ago when the last Congress convened . . . . The time for waiting for jobs has passed. The time for action for jobs is at hand . . . . The only real recovery is one that puts millions of unemployed Americans back to work."

O'Neill noted that the House leadership worked with the Reagan administration and the Republican-controlled Senate in pushing the highways bill through the lame-duck session, and said he hoped there would be similar cooperation when legislation to shore up the Social Security system comes up this year.

"This will be difficult legislation," said O'Neill. "But no legislation is more necessary in 1983 than this."

House Majority Leader James C. Wright Jr. (D-Tex.) was the only Democrat to speak during the hour-long debate on the controversial rules changes, which had been approved unanimously by the Democratic caucus, and were opposed on the floor by only two Democrats: Gramm and Rep. Larry McDonald of Georgia.

Wright said that there were 50 riders attached to appropriations bills in 1980, and that they were consuming too much of the House's time.

"There isn't anything sinister in the proposed change," said Wright. "Several things have conspired to disrupt and undermine the normal authorizing process of Congress. All this does is try to return a bit of the historic prerogative to that process."

Minority Whip Trent Lott (R-Miss.) said the rules changes amounted to a return to the days of "Czar Speaker and King Caucus," when the minority party was virtually powerless to affect the flow of legislation in the House.

Said Lott: "The proponents of these changes seem to be saying, 'Save us from ourselves, save us from having to vote on the issues, make our decisions for us.' This isn't the people's democracy at work. It's cultism and wimpism at their worst."

Along with restricting rider amendments, the rules changes would give more power to the speaker in bringing up legislation and permit three committees--Appropriations, Armed Services and Permanent Select Intelligence--to hold closed sessions for as much as six straight days by a single vote.