New car inventories have swollen to the worst levels since the original Arab oil embargo, forcing American automakers to consider cutting production still further and laying off thousands more workers.

More than 125,000 auto workers already have been furloughed because of sluggish sales, and the United Auto Workers Union expects that number to jump to 140,000 next month because of layoffs already announced.

Additional layoffs are forecast by industry analysts, based on new reports of unsold cars and the automakers' production plans for the next three months.

American auto companies say they will build about 1.86 million cars in the first quarter of 1980, Dow Jones News Service reported yesterday. That would be almost 23 percent fewer cars than Detroit's assembly lines turned out in the same period a year ago.

Even the 1.86 million-unit forecast is optimistic, compared with the 1.76 million-unit production expected by Automotive News, the trade newspaper.

If American car factories do turn out about 1.8 million cars in the first quarter, it will be the auto industry's worst quarter in five years and one of the three worst periods in the past decade and a half.

Production bottomed at 1.3 million units in January, February and March of 1975. First quarter auto output fell to 1.8 million units only two other times in the past 15 years -- in 1970 and 1974.

Just as layoffs are triggered by production plans, production plans are determined by the backlog of unsold cars, and that, too, is approaching record levels.

Estimates of the automakers' inventories now vary from 1.76 million by Automotive News to 1.73 million by Wards Automotive Reports, the other big industry source. Both estimates show increases of about 30,000 cars since November and about 50,000 cars since a year earlier.

But more important than how many unsold cars there are is how long it will take to sell those cars at the current selling pace, analysts say.

Estimates are that the unsold cars would last about 74 days. A 60-day supply is considered normal at this time of year. The supply was 65 days a month ago and only 56 days a year ago.

The days' supply figure is growing faster than the actual number of cars in the inventory because the pace of sales slowed in November and probably will have slowed still further when the final December figures are in.

Auto sales traditionally are very strong in October and November -- after the new models come out -- then drop off in December and don't pick up again until March.

Assuming that pattern prevails, the backlog of unsold trucks. Wards puts dramatically in the next two months. Even the 1.8 million production planned by Detroit is still about 100,000 cars more than the 1.7 million auto sales projected by industry analysts.

Also growing and adding to the motor vehicle industry's woes is the backlog of unsold trucks. Wards' puts the November truck inventory at 845,000 units, a 95-day supply, up from 727,000 units -- 56 days' worth -- a year ago.

The truck decline is so dramatic because 1978 was the best year ever for truck builders. By Dec. 1 of 1978, the industry had produced 3.6 million trucks; this year the output for the first 11 months of the year was just over 3 million units.

The 20-to-22 percent decline in car and truck sales corresponds to about a 17 percent drop in auto industry production employment.

The industry has about 757,000 hourly workers.The 126,000 workers now on furlough and the 140,000 projected to be on the streets by next month is still far short of the peak unemployment of 300,000 reached during the 1974-1975 recession.

The auto layoff figures include only workers who have been placed on long-term furlough. Most of the industry's plants are closed this week for a Christmas vacation that also is helping the industry reduce its inventories.

The president of Volkswagen of America, James W. McLernon, predicted yesterday that total U.S. auto sales for 1980 -- including imports -- will reach 10.4 million.

VW's forecast is the second highest in the industry so far. General Motors is predicting a 10.6 million-unit year, Ford 9.5 million and Chrysler 9.25 million. American Motors has not issued a forecast.