The question isn't so much "what is Sheridan girls" as it is "who are the Sheridan girls." They are first of all, the sisters with whom Leila is going to the ball. They are secondly, the sisters of their brother Laurie (usually short for Laurence). Thirdly, they all are Leila's cousins: "This is my little country cousin Leila. Be nice to her."
The Sheridans and their cousin Leila are on their way to a ball, the first ever for Leila. She had been raised in the country without benefit of society since their "nearest neighbour was fifteen miles," but now we are to infer that she and her mother have moved to the city as she begs her mother "to ring up her cousins and say she couldn't go [to the ball] after all." The Sheridan girls' names are Meg, Jose, and Laura.
But every single thing was so new and exciting [to Leila] ... Meg's tuberoses, Jose's long loop of amber, Laura's little dark head, pushing above her white fur like a flower through snow.
the sheridan girls are leila's cousins
Leila and her cousins.
Obviously, Laura, Meg and Jose.
She is Leila.
She was on the way to her first ball. In the taxi she imagined that she sat with an unknown young man. The Sheridan girls thought it was strange that she had never been to a ball. Leila tried to stay calm, but she was very excited about this new experience.
Exactly when the ball began Leila would have found it hard to say. Perhaps her first real partner was the cab. It did not matter that she shared the cab with the Sheridan girls and their brother. She sat back in her own little corner of it, and the bolster on which her hand rested felt like the sleeve of an unknown young man's dress suit; and away they bowled, past waltzing lamp-posts and houses and fences and trees.
"Have you really never been to a ball before, Leila? But, my child, how too weird--" cried the Sheridan girls.
They arrived at the drill hall, where the ball was. There were lights and happy couples everywhere in the streets. Inside, the girls went into the Ladies’ room. It was crowded with girls getting ready for the ball. They were putting on powder, hair pins, ribbons.