The Old woman was an unnamed old woman who was almost hit by Homer driving a truck.
In another episode homer stole a pie from a woman's windowsill who may have been this woman. She is seen yelling unintelligible stuff waving a rolling pin in the air.
While Homer was driving Red Barclay's truck to Atlanta, he learned that there is the Navitron Autodrive system in the trucks, so vehicles can drive themselves. He showed off the system to Bart by directing the truck on an old woman, slowly walking on the road. Homer didn't hold a wheel and Bart told him to stop. The system then started working and the truck sidestepped the old woman by itself.