When President Jaafar Nimeri meets President Reagan on Monday he is expected to invoke last week's antigovernment demonstrations here to bolster his case for unfreezing nearly $200 million in U.S. aid to Sudan, according to diplomats here.

Many Sudanese suggest that Nimeri purposely tolerated the demonstrations -- which began before he left for Washington Wednesday -- to underline demands for lifting the stringent financial conditions blocking disbursement of the funds.

The university students who led the demonstrations last week denounced alleged dictation by the International Monetary Fund and the World Bank. In fact, economists and diplomats here noted, it is the Reagan administration -- and not those Washington-based international institutions -- that has the power to resume aid to its biggest recipient in black Africa.

That political message -- backed by shouts of "We are hungry" from the unemployed youths who tossed rocks through bank, shop and hotel windows and set cars on fire -- also underlined Sudan's growing fragility.

Many times before in his 16 years in power the supremely self-confident Nimeri deliberately has left the country at the height of a major crisis to put his own people and his foreign allies on notice that without him Sudan could collapse. This time he plans to be abroad 16 days for official visits to the United States, Egypt and Pakistan.

Beset by civil war, a massive influx of foreign refugees, drought, famine and a disastrously mismanaged economy, Nimeri nonetheless can point to tough decisions he has taken recently, apparently at U.S. insistence.

In the four weeks since Vice President Bush visited Africa's largest country, Nimeri has announced a series of long delayed political and economic reforms. Following up on a February decision to devalue the Sudanese pound from 1.3 to 2.5 to the dollar, he raised bread and gasoline prices by roughly 60 percent.

Politically, he again braved the wrath of his fellow Arab League members by allowing the Central Intelligence Agency to use U.S. military aircraft to airlift most of the remaining 900 Ethiopian Jewish refugees to Israel. Several thousand of the Falashas had been airlifted between November and early January in commercial aircraft.

Nimeri also cracked down on the Moslem Brothers, the fundamentalist Islamic sect considered chiefly responsible for persuading him 18 months ago to institute sharia, or koranic law, not just on the Moslem north but also on the Christian and animist south. But the arrest of Moslem Brothers leader Hassan Torabi and many of his followers two weeks ago has yet to convince Nimeri to abrogate sharia, although he promised to review its sentences which involved many amputations of limbs.

Abrogating sharia is believed essential by many Sudanese inside and outside the government if southerners are to abandon their insurrection against Nimeri. Only last week, however, the chief justice of the sharia court system and 30 of his judges visited three major southern towns to choose buildings for their religious tribunals.

With Army and riot police patrolling Khartoum and its sister cities of Omdurman and Khartoum North, no fresh violence has been reported since Thursday. Although the capital's politically influential doctors are on strike to protest alleged police brutality during the demonstrations that claimed as many as eight lives, a rumored organized protest by Sudanese professional organizations has yet to take form.

Many Sudanese and diplomats question whether security forces would dare break up a general strike and peaceful demonstrations called by such establishment organizations. But observers speculated that the associations of doctors, lawyers, engineers, bankers, teachers and accountants had already lost so much of the momentum created by last week's demonstrations that they may have forfeited their best chance in years to unseat Nimeri.

Government newspapers have reported that since the demonstrations began in Omdurman Tuesday, 2,641 persons have been arrested, of whom 854 were condemned to lashing under sharia, fined or given suspended sentences. The others, apparently mostly vagrants and unemployed teen-agers, are being taken out of the capital and told not to return. Army trucks full of young men were seen crossing Khartoum today.

But the stakes in Washington remain whether Sudan has satisfied the administration -- especially the Treasury Department -- that it has gone far enough to put its financial house in order to warrant support.