Mehlhaff, who the Saints drafted last spring but cut after training camp, was brought back to replace injured kicker Martin Gramatica in Week 6. In three games, Mehlhaff was 3-for-4 on field goals and 9-of-10 on extra points.
Graham replaced Steve Weatherford, who was cut after the Saints' loss to Carolina on Oct. 19. Graham's only appearance for the Saints came last Sunday in London. He punted three times, averaging 42 yards.
"We were impressed with both Garrett and Glenn throughout the competitive sessions and we will continue to evaluate the positions closely throughout the remainder of the season," Saints general manager Mickey Loomis said.
Hartley signed as a rookie with the Denver Broncos in April and was released prior to training camp.
The Seattle Seahawks signed Pakulak as a rookie free agent in 2003. He had stints with Pittsburgh, Atlanta, Oakland, Tennessee and Chicago but has not played in a regular season game.
The Saints also signed defensive back Tanard Davis to the practice squad.