They are first seen chasing Lady, who is wearing a muzzle on her face. They corner her in an alley, but Tramp steps in and saves Lady by fighting off the stray dogs. They eventually run off yelping and are not seen throughout the rest of the film.
The Stray Dogs' names weren't mentioned, but in the art gallery their names were Alfred, Ford and Rufus.
The Stray Dogs also take on the role as the Man's hunting dogs in Bambi, where Bambi rescues Faline from a pack of hunting dogs, which is what Tramp did to save Lady from a pack of stray dogs, eventually defeating them.
In addition, the barking sounds used for the Stray Dogs were the same ones used for the hunting dogs.