Challenges to President Jaafar Nimeri's government escalated today, as demonstrations against him continued and a burgeoning general strike closed down Khartoum Airport and much of the rest of the city.

This correspondent, deported without explanation early today on what apparently was one of the last flights to leave the country, heard loudspeaker announcements canceling all operations of the national carrier, Sudan Airways. Later diplomatic reports reaching western capitals said that airline workers had gone on strike, along with many other government employes.

Overseas telephone and internal and international telex lines remained cut for the second day, although it was unclear if this was due to striking workers or the result of government nervousness about letting the outside world know the extent of the strike.

Nimeri, at the midway point of a 16-day foreign tour, was still in Washington with no plans to return immediately to Sudan, State Department sources told staff writer David B. Ottaway. The sources said they had received reports today from Khartoum of large numbers of people gathered in the streets in groups of 2,000 to 4,000.

The sources said that the demonstrations, which follow a series of strikes begun last week to protest government economic measures, had become increasingly political in nature.

The militant opposition tone was set yesterday when good-natured crowds of mostly middle-class and middle-aged Sudanese, estimated by western diplomats at 20,000, defied a government ban and peacefully demonstrated in downtown Khartoum, demanding Nimeri's resignation and a return to civilian, democratic rule.

The spreading civil disobedience underlined the lengthening odds against Nimeri, who has remained in power for 16 years, in large part thanks to his opponents' lack of cohesion.

However, many Sudanese say they have learned not to underestimate the durability of the president, who has survived many attempts to overthrow him.

Of particular significance yesterday, however, was the absence during more than three hours of demonstrations of either the police or the armed forces, who apparently were loath to intervene in a purely political dispute.

The tactics of the striking professionals -- doctors, lawyers, engineers, university professors, bank employes, insurance workers -- and students are to win over the armed forces and police, which they claim constitute Nimeri's remaining support.

It was left to Nimeri loyalists among the uniformed riot police -- and security forces in civilian clothes -- to contain the demonstrators, who proved their planning skill by appearing at many points at the same time as if by arrangement.

All morning the demonstrators played cat and mouse with helmeted riot police, who displayed retraint in using tear gas to keep them from reaching the presidential palace facing the Nile River.

Constantly breaking into groups of several hundred, then forming again into crowds of several thousand, the demonstrators vastly outnumbered the audience the government was able to muster Tuesday in front of the palace in its own support.

At one point, reporters saw riot police, armed with long bamboo clubs and rifles, firing a dozen rounds over the crowd's heads, near the Meridien Hotel on Qasr Avenue. But there were no known gunshot wounds or fatalities and apparently relatively few arrests, judging by reports from reporters on the scene. Symptomatic of the political mood was the presence in the crowd of several of the old yellow, green and dark blue flags, which Nimeri replaced when he took over in 1969.

Unlike the three days of disturbances in the capital area last week, when unemployed teen-agers committed widespread acts of vandalism, yesterday the older, more affluent demonstrators conducted themselves with dignity and caused no known material damage.

Some Sudanese said yesterday that they had decided to demonstrate when they realized that the state-run television was running old footage of the government-sponsored Tuesday meeting to hide the poor turnout. Other demonstrators ridiculed what they called the government speakers' "worn-out rhetoric."

"Blaming the communists and the Moslem Brothers," the recently disgraced Islamic fundamentalists who had exerted great political influence, "for all the country's troubles may go down fine when Nimeri talks to President Reagan in Washington," one demonstrator said, "but here we know better. It sounds like the shah blaming his troubles on the same kind of opposites just before he fell."

The professors and other demonstrators said they hoped to duplicate the events of 1964. Then in the so-called "October Revolution," university professors led other intellectuals in forcing the resignation of the military government headed by field marshal Ibrahim Aboud. Among the slogans chanted by the crowd, were "Down, down with the U.S.A.," "The scoundrel Nimeri has gone to the United States while we are starving," "We won't be ruled by an American spy," and "With our blood and spirit we will defend the Sudan."

But despite the anti-American slogans, the mood was clearly focused on internal politics and directed against the president, who faces civil war, gigantic financial problems, a massive influx of refugees from Ethiopia and the threat of famine due to prolonged drought.