A stifling heat wave continued to hang over much of the country yesterday and was gradually spreading eastward, bringing with it discomfort, damage to crops, and death.

The number of heat-related deaths during the three-week siege of blistering weather was estimated at about 764. Missouri, Texas, Alabama and Arkansas were the hardest hit of the 17 states where such deaths have been reported.

The heat wave, which began in the Southwest and south central plains states, continued to spread into the East yesterday, as evidenced by the record 103-degree temperature recorded at Washington National Airport. National Weather Service officials said they could predict no relief for the increasingly larger portion of the country being affected by the heat until next week at the earliest.

Other afternoon temperatures recorded yesterday included 100 in Atlanta, 103 in Birmingham, 102 in Fort Worth, Little Rock and Oklahoma City and 101 in Springfield, Mo. Dallas was in its 24th day of 100-degree-plus temperatures.

Meanwhile, violent storms and tornadoes slashed across the large portions of the Midwest from Oklahoma to Minnesota yesterday, killing at least three people and disrupting electrical service to thousands of homes and businesses.

Winds of 114 mph were recorded at the Eau Claire, Wis., airport. A curfew was imposed in the city to prevent looting of damaged businesses, and Gov. Lee S. Dreyfus declared a state of emergency for four west central Wisconsin communities.

Elsewhere in the Midwest, the same series of storms left as many as 100,000 customers without electricity in Minnesota and shut down Chicago's O'Hare International Airport, the world's busiest, for an hour.

The storms even managed to intrude on the peace and harmony that has marked the Republican National Convention in Detroit. Vice presidential hopeful George Bush was forced to cut short a speech to a GOP delegation at a hotel near the Detroit airport and take refuge in a secure room after the storm knocked out power and demolished a brick wall of an auditorium being built at the hotel.

The spread of the heat wave into larger sections of the Midwest Tuesday and yesterday increased concern over the likely effect on crops, farm income and food prices.

The heat spell has already driven up the price of grain used to feed livestock, and is expected to be reflected in higher prices for meat later in the year.

Agriculture experts said the heat wave was reaching the cornfields of Iowa and Illinois at the worst possible time, when the corn is pollenating. Temperatures of 95 degrees or higher inhibit the process, leaving the crops without kernels.

There were no reliable estimates of overall crop damage caused by the heat wave. But in Georgia, state officials said the heat had destroyed more than $100 million of the state's corn crop. They said as much as $350 million worth of soybeans could also be lost if there is no relief soon.

In Arkansas, officials said soybean farmers could lose $150 million or more.

The worst of the heat wave continued yesterday in the region from Missouri south to Texas and southwest to New Mexico. The death toll from the heat in Missouri stood at 101, highest in the nation, and officials there and in neighboring Kansas were comparing the siege with the heat waves that struck the region in the Dust Bowl era of the 1930s.

"We're approaching something very similar to the mid-1930s, a landmark for heat and dryness," said Phil Shideler, chief meteorologist for the National Weather Service in Topeka.

There was no age breakdown on the heat-related deaths, but local officials stressed that the elderly are particularly vulnerable. In addition to having generally more fragile health, the elderly, officials said, are often afraid to leave their homes for air-conditioned facilities being provided for them in some communities, and some are so fearful of high utility bills that they refuse to use air conditioning or fans in their homes.

The Carter administration sought to ease the burden on low-income families by making $6.73 million available to the poor in six states. The money, emergency funds of the Community Services Administration, the nation's antipoverty agency, is to be used to pay utility bills, buy fans and air conditioners and provide transportation to relief centers.