The narrator describes how Dame Van Winkle would respond to one of Rip's shrugs. This provokes a "fresh volley" from his wife. "Volley" can mean to kick or hit a ball (as in tennis or volleyball) but here it probably means a discharge of bullets. The narrator uses the metaphor of bullets to describe the way Dame Van Winkle scolds and screams at Rip.
When the narrator is discussing how the dog, Wolf, loses all of his courage upon entering the house, he says Wolf "sneaked about with a gallows air." A gallows is a structure used for hanging. Dame Van Winkle scolds Rip and the dog so often, the dog behaves as if he is at an execution.
At the end of the story, the narrator discusses the changes that have occurred during Rip's long sleep. He notes that the country had "thrown off the yoke of old England." A yoke is a piece of wood placed upon an animal so the animal can pull something or plow a field. It is a burden on the animal and this is the meaning here. The narrator also adds that Rip has lost the "yoke of matrimony." The country is free (independent) because it is no longer burdened by England. Rip is also more free and independent because he is free of his wife's nagging.