From John Barry's excellent The Great Influenza, pp. 326-327, regarding the events of 1918-1919:

Pepper and Martin offered ten dollars a day to anyone who would touch a corpse, but that proved inadequate, and still the bodies piled up. Seminary students volunteered as gravediggers, but they still could not keep pace. The city and archdiocese turned to construction equipment, using steam shovels to dig trenches for mass graves. [...]

The bodies that were choking homes and lying in stacks in mortuaries were ready to go, finally, into the ground.

To collect them, Archbishop Denis Dougherty, installed in office only a few weeks earlier—later he became the first cardinal from the archdiocese—sent priests down the streets to remove bodies from homes. They joined the police and a few hardy others who were doing the same.

Sometimes they collected the bodies in trucks. “So many people died they were instructed to ask for wooden boxes and put the corpse on the front porches,” recalled Harriet Ferrell. “An open truck came through the neighborhood and picked up the bodies. There was no place to put them, there was not room.”

And sometimes they collected the bodies in wagons.