The 1980 presidential campaign has gone into its final stage with President Carter and Republican challenger Ronald Reagan in a virtual deadlock in seven key states, according to a series of Washington Post polls completed last week.

The polls, taken between Sept. 26 and Oct. 5, showed Carter significantly ahead in New York, but the rivals within three points or less of each other in Texas, Pennsylvania, Illinois, Ohio, New Jersey, Florida and Michigan. With a possible sampling error of plus or minus 4 percent in the surveys of 600 persons who said they were registered voters in each state, the race in every one of the states except New York must be considered a deadlock.

The seven tossup states have 159 of the 270 electoral votes needed for victory. California, the largest state, with 45 electoral votes, was not included in the roundup. Other surveys have shown Reagan ahead there.

In 1976, Carter carried four of the seven swing states -- Texas, Ohio, Pennsylvania and Florida. Had the 95-to-64-vote ratio over Gerald R. Ford in those seven states been reversed, Ford would have been elected by one vote. Thus, the extremely close races indicated in those states by the Post polls point to the possibilitity of an equally close national election this time.

The survey dramatizes the importance of independent candidate John B. Anderson as the race enters it final three weeks, Anderson's support ranges from a low of 6 percent in Texas to a high of 17 percent in in his home state of Illinois. But in every one of the seven big swing states, it is several times as large as the current margin of difference between Carter and Reagan.

The Post's polls also show an exceptionally high undecided vote in most of the states. The makeup of that vote suggests that Carter may have a slight advantage over his rival in the showdown battle for those states.

The percentage of those undecided ranges from 16 percent in Texas and 17 percent in Florida to a high of 27 percent in New Jersey. But that is only the beginning of the story of the uncertainty overhanging the outcome of the election in these seven states.

Overall, 22 percent of the voters who expressed a preference for Carter, Reagan or Anderson said they were "not at all strongly" behind the candidate of their choice. When that group is added to those who said they were undecided, almost 40 percent of the electorate in the seven states may be seen as available for persuasion in the remaining days of the campaign.

On the face of it, Reagan is slightly more secure against last-minute shifts than Carter. While 23 percent of Carter's supporters say they have only a light attachment to their candidate, only 20 percent of Reagan's backers say they are equally loose.

The biggest bloc of potential defectors is in the Anderson camp: 30 percent of the Illinois congressman's supporters characterize their presence as slight. The battle for those "loose" Anderson votes will be fierce in the windup period of the campaign.

By grouping together those voters who have no preference or only a slight attachment to a candidate, it is possible to draw a collective portrait of the target voters in the key states.

Democrats and independents predominate. Of those with no preference or only slight preference, 42 percent call themselves Democrats, 36 percent independents and 22 percent Republicans. Repubulicans rate 8 points higher among those with firm convictions, which means that Reagan has nailed down a larger share of his party's vote than Carter has, but now must forage primarily among those who do not share his political affiliation.

The same thing is true when the ideological yardstick is applied to these target voters in the key states. People who describe themselves as conservatives make up 32 percent of the voters with firm preferences (and Reagan is, of course, their favorite), but they comprise only 25 percent of the target voters, the same portion that call themselves liberals.

But the biggest bloc of undecided and lightly committed voters is, not surprisingly, the people who consider themselves right in the middle of the political spectrum. Overall, 43 percent of the self-described independents and an indentical percentage of the self-described moderates fall into this group. There are more woman than men among the undecided and uncertain.

A special target group is made up of Jewish voters, 54 percent of whom say they are uncertain how they will vote or are uncommitted to their present candidate.

In all these respects, the target voters appear to be people who are tilted somewhat in Carter's direction, by their predilections or characteristics. They also have a slightly better personal estimate of Carter's abilities than of Reagan's though neither man can take great comfort in his judgment.

Among the undecided or lightly attached independents in these states, for example, 46 percent say Carter is a better president than he gets credit for being, while 42 percent say that Carter "just can't cut it" as president.

Among those same voters, 35 percent agree with the statement that Reagan is "well-qualified to be a good president," but 48 percent disagree. Thus, Carter has shaky plus-4 rating and Reagan an ominous minus-13 rating on a pair of personal evaluation questions which, among committed voters, correlate highly with the voting decisions.

There is one negative for Carter among the target voters, however. As a group, they are more pessimistic about their economic future than are most of the voters who have made firm candidate decisions. Among those with strong preferences, optimists about the financial future outnumber pessimists by 46 to 15 percent. Among the target voters, those who think things will get better outnumber those who think they will get worse by only 9 points, 34 to 25 percent.

Reagan is hammering hard on Carter's "mismanagement" of the economy, and, unless a fresh wave of optimism sweeps over the target voters, they should be much more receptive to his argument than those who have already cast their lot firmly with one of the candidates.

Among the findings in the Post's polls was one that suggests that Sen. Edward M. Kennedy (D-Mass.) could play a crucial role as the campaign winds down by inducing -- or not inducing -- former Kennedy supporters to shift to Carter.

A significant number of those polled described themselves as having been Kennedy supporters at the time of the primaries in the seven states, in all probability enough to turn the election in several states if the race remains as close as it appears to be right now.

These Kennedy supporters were sharply split when asked whether they felt he "really wanted Carter to be reelected or not," and their voting intentions seemed to reflect that split. Those who felt Kennedy was behind the president were strongy for Carter, with up to 80 percent saying they were supporting his reelection. But a majority of those who felt Kennedy was not truly behind Carter failed to endorse the president, tending to say they were either for Anderson or were undecided.

The views of many erstwhile Kennedy supporters may have been captured in the words of one of the almost 5,000 people interviewed, a 48-year-old actress from Ohio. "Carter is very indecisive," she said. "He knows nothing about politics."

As for Reagan, she said, he has "a lack of experience" and "narrow view," and his age works against him as well. This woman, who voted for Carter in 1976, says she is undecided now but that she is "absolutely certain" she will vote one way or another when the time comes.

She also says she feels that Kennedy is not working hard for Carter's reelection. While there is no way of knowing, she and thousands of others like her in the key states seem likely to be moved by whatever role Kennedy chooses for himself between now and Nov. 4.

Finally, it should be pointed out that, while the seven swing states polled by the Post may be the key to the election, they are not the whole story. A national survey in late September, based on polls and the judgements of political observers, put Reagan 25 electoral votes ahead of Carter in the other 43 states and the District of Columbia.

In those states, Reagan was credited with 176 electoral votes and Carter with 151, while 52 were in the tossup category.