Four hundred eight days before the first caucus in Iowa, 416 days before the first primary in New Hampshire and 550 days before some Democrat will be nominated for president, seven Democratic hopefuls came here today to audition their talents at the state Democratic convention.

A straw poll of delegates taken by the Los Angeles Times during the last 11 days showed California's favorite-son candidate, Sen. Alan Cranston, the favorite of 40 percent. Former vice president Walter F. Mondale was second with 15 percent and Sen. Edward M. Kennedy (Mass.), who has withdrawn, third with 7 percent.

Sen. Gary Hart (Colo.) had 5 percent, Sen. John Glenn (Ohio) 4 percent, Rep. Morris K. Udall (Ariz.) 2 percent, Sens. Dale Bumpers (Ark.) and Ernest F. Hollings (S.C.) 1 percent each, and 25 percent were undecided.

On a separate straw vote, taken on the convention floor after all the speeches today, Cranston received 783 of 1,322 first-place votes, or 59 percent, with Mondale taking almost 23 percent and the others dividing 17 percent.

But on the floor today, Mondale, who leads the national polls, led on the applause-meter, being challenged only by Cranston, whose operatives had made a major effort to use this convention as a springboard to his official announcement early next month. Mondale was the second choice of almost half of the Cranston voters in the Times poll, which reached 1,416 of the approximately 1,700 delegates, and he led the field with 23 percent of all second-choice votes.

Of all the active contenders, the only absentee today was former Florida governor Reubin Askew.

In an eight-hour procession of alternating speeches and press conferences, the rivals vied for original ways to condemn the record of the Reagan administration and promise progress in arms control and economic growth.

A favorite pledge, offered by Cranston, Hart and Mondale, was to go directly from the inaugural platform in 1985 to a summit conference on nuclear arms control with Soviet leader Yuri V. Andropov.

The candidates all made vows to the Equal Rights Amendment, Dr. Martin Luther King Jr.'s birthday and such causes as education, environment and scientific research.

There was little news in the day's speeches, as all of the candidates recited their favorite applause lines and wended through rounds of caucuses representing the cornucopia of ethnic and interest groups in the California party.

But the fact that all of them flew here--Glenn even breaking off a Latin American tour for the Senate Foreign Relations Committee--gave evidence of the extraordinarily early start on presidential politicking.

Party rules changes adopted last year moved the first delegate-selection caucus in Iowa back five weeks from its 1980 date to Feb. 27, 1984. The first primary in New Hampshire was forced back a week to March 6, 1984. The purpose of the changes was to shorten the campaign season that will climax July 18, 1984, with actual balloting for the Democratic presidential nomination.

But, as Mondale told a news conference Friday, the "openness" of the selection process, the need to contact thousands of activists who participate in primaries and caucuses and the need to raise campaign money in small amounts from thousands of individuals make it necessary for the Democrats to start campaigning 18 months before the convention.

Left unsaid by him, but equally important, was the fact that the surprise withdrawal from the race of Sen. Edward M. Kennedy (D-Mass.) last month catapulted Mondale into the front-runner's role, with Glenn a challenging second and the others scrambling to catch up.

Udall, the 1976 runner-up to Jimmy Carter, is still weighing his entry into the race, as is Bumpers. The others are expected to become formal declared candidates within the next few weeks.

Udall told a news conference he would release "in a few days" a doctor's report on Udall's case of Parkinson's disease. Udall said the report would testify that he could stand the strains of a long campaign and of the presidency. But he conceded that some advisers are telling him he is "too late" in getting into the race, and he sounded uncertain about his decision.

Perhaps for that reason, he did not immediately reject the semi-serious offer Mondale made in his speech to appoint Udall either secretary of the interior or head of the Environmental Protection Agency "when I become president."

"That's the best offer I've had so far," Udall said.

The "job offer" to Udall was one of many ways in which Mondale exploited his position atop the polls, at least for now, to separate himself from the rest of the Democratic pack. In an evangelical speaking style he uses more frequently than in the past, Mondale repeated the oratorical victory that he scored at last summer's Democratic "mini-convention" in Philadelphia.

Whether attacking "special interest money that is paralyzing our government" or assailing the Reagan administration for "giving tax breaks to the rich and cheese to the poor," Mondale seemed able to get the delegates up and cheering almost at will. He made no reference to Carter, who picked him from the Senate for vice president in 1976, but drew cheers when he pledged to carry on the civil rights crusade of "my mentor and friend, Hubert H. Humphrey."

Cranston, who had worked harder than anyone else to line up his home-state delegates' support in the straw poll, also pepped up his speech with at least 40 guaranteed applause lines. He characterized the Reagan administration as a "plutocracy of plunder, power and privilege . . . a government of the rich, by the rich and for the rich."

The afternoon speakers had varying degrees of success in holding the attention of the restless 2,500 delegates and observers.

Udall was greeted warmly by the largely liberal crowd and scored well with his jokes. Hollings had more trouble holding their attention, as he coupled his criticisms of Republican economic policies with a warning to Democrats to avoid the big-spending programs of the '60s and '70s.

Bumpers was followed more attentively and drew real cheers for how he depicted his role in leading "the lonely and losing fight . . . to keep James Watt from being confirmed as secretary of the interior."

Bumpers said, however, that he is still in the "possible prospect" category, uncertain whether he can raise the money and assemble the staff for a late-starting campaign.

Hart gave a speech as long as Cranston's half-hour oration but including far fewer applause lines. His high point may have been his promise to the large group of former Kennedy backers in the hall that, although Kennedy is not a candidate, "we are resolved that the principles he has stood for will be represented in the Democratic victory of 1984."

Hart's discursiveness set the stage for a favorable showing by Glenn with a brief, punchy speech that closed the long day. He was cheered when he said Reagan might ask the country to "stay the course, but I say he's flunked the course--with failed policies that have brought this country to the brink of economic disaster."