Thousands of women and children marched through Lodz, Poland's second largest city, yesterday chanting against food shortages and carrying banners that read, "We want to eat."

New threats of strikes and protests spread to all corners of the country. The Warsaw chapter of the independent union federation Solidarity declared a regional strike alert starting Monday.

The union said that bus drivers and streetcar operators in Warsaw scheduled a three-hour warning strike next Wednesday and that factory workers would strike for two hours.

Solidarity leaders in Lodz, a city of 840,000, said from 8,000 to 10,000 persons marched through the city's center.

Women are an important part of the work force in Lodz, the nation's textile center about 80 miles southwest of Warsaw. Their march capped a fourday series of parades by buses, trucks and other vehicles.

In Warsaw, the capital city with 1 1/2 million residents, the union's local chapter added weight to a mounting number of protests and threats of strikes in smaller cities.

Workers planned hunger marches in seven cities, warning strike at Warsaw's Nuclear Research Institute and a boycott of rationing coupons at some of Poland's largest factories. They also scheduled a rally outside the parliament building today to present a petition asking for prompt economic reforms and a resolution to the food problems.

No strikes were reported, but anger over the food situation has sparked several since the first organized hunger march in Kutno, near Lodz, last Saturday.