Frustrated at almost every turn as they try to adjust to the unfamiliar role of the loyal opposition, Senate Democrats are groping for new strategies, new ideas, a new image -- everything, it seems, except new leaders.

Rumbles of dissatisfaction with the leadership of Minority Leader Robert C. Byrd (D-W.Va.) recur from the right as well as the left, yet Democratic senators rally to Byrd's defense at the slightest suggestion of an imminent uprising.

Although his position is apparently secure through the end of next year, nothing is clear beyond that. Some senators do not rule out a change in leadership in 1983 if, as one of them put it, "we can ever get our own act together enough to decide where and how we want to be led."

For one thing, Senate Democrats have reelected Byrd as party leader, along with Californian Alan Cranston as whip, for the duration of the 97th Congress, which runs until after the 1982 congressional elections.

Any overt challenges in the meantime would only give additional public display to the divisions that beset the party in Congress as it seeks to cope with an apparently popular Republican administration and its seemingly gung-ho GOP congressional supporters.

"There are times," lamented one liberal Democratic senator who's not particularly enthusiastic about Byrd's stewardship, "when the less said the better."

There is also the question, "Who else?," which helps explain why Byrd was reelected without open dissent after November's Democratic debacle at the polls, when Democrats were thrust into a minority in the Senate after a quarter-century of ruling the roost.

There was talk then of a challenge, but it never materialized, in part because no clear consensus developed for anyone else. The party is sufficiently divided in ideological terms, with a resurgent right wing challenging a weakened liberal flank, to make a consensus difficult, even without the crosscurrents arising out of personal political ambitions.

"Who are we going to turn to?" one liberal senator asked impatiently. "To get rid of someone you have to have a viable alternative, and look around here, there just isn't one."

The silver-haired, 63-year-old Byrd came to the leadership ranks in the Senate by assiduous attention to the needs of his colleagues and mastery of congressional procedures.

These qualities are valuable for a minority as well as a majority, but some senators complain that Byrd lacks the dynamism and public presence that a party on the rebound needs to articulate its policy alternatives. Some also complain that policy has never been Byrd's strong suit.

"He's procedure man, not a policy man," said a conservative Democrat who feels the party needs more policy direction.

"He's a technician, not an idea man, not an articulate spokesman on issues," said an aide to a more liberal Democratic senator who also yearns for a more forceful Democratic response to Reagan administration initiatives. f

The problem is that these two Democrats have profoundly different ideas of what Democratic policy should be.

In succeeding the more relaxed Mike Mansfield, Byrd has made himself a round-the-clock leader, setting a work standard that tends to shrivel the ambitions of some of his less workaholic colleagues.

Moreover, there is a big difference between the perks and glories of a minority leader and those of a majority leader, especially when House Democratic leaders still run things on their side of the Capitol.

Finally, an ambitious politican might be tempted to wait for more auspicious times to speak for Democrats, especially if, as some of them predict, the glow of the Reagan administration does not last.

Although Byrd started out four years ago with more critics on his left than on his right, he moved swiftly to win them over. This year the more visible restiveness has come from the right, where conservative-leaning Democrats formed a caucus early in the session in part to nudge the leadership their way.

Some of them were particulrly incensed by Byrd's push of fair-housing legislation in the post-election session last year, interpreting it as a move to mollify liberals such as Sen. Edward M. Kennedy (D-Mass.) while their own political lives were made more difficult.

But since then Byrd has appointed conservatives as well as liberals to a party task force that is preparing strategy for dealing with President Reagan's economic program, and dipped into the left as well as the right for spokesmen to give the Democratic Party's televised response to the Reagan program.

"There's been general satisfaction with his leadership," said Sen. David L. Boren (Okla.), one of the principal organizers of the group.

Byrd also drew praise for stage-managing the public humbling of Senate Republicans when Reagan had to propose an increase in the government's debt ceiling shortly after he and the new Senate majority took office.

In some of the best theater Congress has put on in recent years, Democrats cast a steady stream of "no" votes until the Repubicans, many of whom won office campaigning against debt-ceiling increases, coughed up enough votes to pass Reagan's proposal.

The exercise, which lifted Democratic spirits at least temporarily, also had the effect of making Byrd and other Democratic leaders look a little more comfortable in their new-found minority role.

Few have looked less comfortable than Byrd, who hails from one of the nation's most Democratic states and has not served in the minority since his first days in the House in the early 1950s.

"He's been real nervous in the saddle . . . sort of insecure. . . . He's always having meetings," said a colleague. For a time, he needled Sen. Howard H. Baker Jr. (R-Tenn.), his successor as majority leader, on the fine points of parliamentary procedure. He also continued his delivery of commentaries on Senate history in the late afternoon or early evening, often a solitary figure addressing a nearly empty gallery.

"It doesn't come easy for any of us," said another Democrat who lost a lot of power when the Senate Democratic world turned upside down this year. "But it's probably hardest of all on him."