John Fishwick, president of the Norfolk and Western Railway Co., has been asked to be a host at one of the six official parties celebrating Jimmy Carter's inauguration Jan. 20 here. There's only one problem: Fishwick has not been invited to the party himself.

Judy Cloe of Arlington, who served as the coordinator of Carter's campaign in Virginia's 10th Congressional District, was asked along with other district coordinators to submit a list of 10 campaign workers who deserved an invitation to an inaugural party. She did. None of them have been invited; nor has she. Her counterpart in the 8th Congressional District, however, has been invited.

A Maryland man - who asked that his name not be used - started campaigning for Jimmy Carter last February, drove more than 27,000 miles in his own car and donated over $700. He has not been invited to an inaugural party. But three Republicans he knows who work for IBM, and who hate Carter, have been invited.

"Of course there have been some areas where we messed up," said inaugural invitations director Curt Moffat. "But there is no cause for alarm. We are doing our best - there is no way we can make everyone happy, and no one is more sensitive to that fact than I am."

To say that some people are not "happy" about not having received inaugural invitations would be an understatement, particularly among the Virginians and Marylanders whose names are left out, ignored by the Carter computer, lost or whose invitations have in some other way been undelivered.

"People over here are furious," said Virginia state Del. Warren G. Stambaugh, who worked as a Carter coordinator in Missouri and has not been invited.

"I'd say there was a minirevolt going on," said Fairfax County Democratic Chairman Emilie Miller, who has not been invited either. The committee lent its office to the Northern Virginia Carter Campaign.

The inaugural committee mafled out 300,000 general invitations - which have come to be known as "y'all" invitations because they are basically a souvenir and don't admit the recipient to anything the public couldn't attend.

Another 25,000 people were to receive invitations to buy two $25 tickets to attend one of the six official inaugural parties (they are being called that instead of "balls"). Roughly 18,000 were invited to buy tickets to sit in the bleahers to watch the parade, and 5,700 were invited to buy two to attend a reception for Vice President Mondale. Still fewer will be invited to buy tickets for the preinaugural concert - but it's the party tickets that everyone seems to really care about.

The list of party invitees was culled from other lists fed into a computer. The computer was programmed to cancel invitations to more than one person at the same address with the same last name. This may be why Stambaugh's wife, Dottie Carter, coordinator in Arlington, was invited and he was not. Each list was "prioritized" as well. Moffat said, with the people ranked in order of importance. Why the Arlington coordinator is considered more important than the coordinator of two congressional districts in Missouri is not clear.

Inevitably, Moffat agrees, there have been problems.

The list of Northern Virginia workers, for example, was "inadvertently misplaced," according to a transition staff spokeswoman, and was found only Wednesday - shortly after a reporter called to find out what was happening. Not to worry, spokeswoman Jane Wales said, the list is now being fed into the computer and the invitations should be going out soon.

But Northern Virginia does not appear to be the only area where Carter workers are variously amused, insulted, furious, worried, hurt, or puzzled at having been left off the invitation list.

Maryland Carter coordinator Arnie Miller said that 80 per cent of the 80 names submitted from Maryland's eight congressional districts did not make the list until he went to inaugural headquarters and "banged on the tables and made a fuss." He checked the computer list himself, corrected it, and now says "I think most of the eregious errors have corrected."

Unfortunately, his assistant during the campaign, Tom Goodwin, whom he asked to help him sort out invitations mix-up, has not been invited either.

There are other examples:

The Rev. Jerry Falwell, a Baptis minister in Lynchburg, who attacked Carter on a television show carried by 260 stations around the country for his interview in Playboy magazine, has received a "y'all" invitation. The unpaid Virginia staff press aide who spent days rebutting the attack has not.

Ellen Berlow, who worked as Maryland state press secretary during the campaign, did not receive an invitation - until she started volunteering at inaugural committee headquarters and told them she had not been invited.

A nun in Iowa, Sister Mary Eugene, said she and four other people set up the Democratic headquarters in Kossuth County and orgnized all the polling, convassing and delivering of bumper stickers in the northern Iowa county. The five people made plane reservations, booked rooms at a hotel here, and friends donated money to pay the sister's way to attend the inauguration. None of them has received an invitation, she said, except for the "'all." But the shopkeeper down the road who did nothing but donate money got one, she said. "We're very upset."

Of two equally ranked coordinators in a Missouri district, one had been a Carter delegate to the Democratic National Convdntion, and the other had not. The one who had not been a delegate was invited.

The workers in the "fighting Ninth" Congressional District of Virginia - which went for Carter although he lost the state by 22,658 votes - have yet to receive anything either, nor have people from Suffolk County, nor many workers in Roanoke. "At least when people call to complain I can say I don't have any tickets either," said Fishwick.

"It's getting embarrassing," said James P. Jones, Democratic party chairman of the Ninth Congressional District of Virginia. "Our Republican congressman (William C. Wampler) has 15 tickets to the parties and since none of the Republicans around here seem much intersted in going, a Democratic friend of mine thought he'd ask him for one. But you really hate to ask a Republican for a ticket to the first Democratic inauguration in 12 years." (All senators and congressmen are given 15 invitations to buy tickets to the inaugural parties.)