Squall parents are Laguna, and Raine. After fighting in the Galbadia Army, Laguna ended up in Whinhill, where Raine took care of him. Ellone lived with Raine, and it doesn't say what was going on with her parents. all you know about them is they lived in the house next to Raine. Laguna and Raine fell inlove, and got married. You don't find out that she was pregnant till Ellone tells Squall that she wanted her Uncle Laguna to be by Raines side, so she could show him her new born baby. Because Ellon was kidnapped, Laguna went to Esthar to find her, when he does, he keeps to his word to his new friends to get rid of Adel, and become the president. doing that ment sending Ellone with one of his friends back to whinhill. when Ellone got there, Raine had died from cancer. so what happened to the baby? Ellone was taken away to Edeas orphanage, the baby must have been to. Ellone looked out for Squall in the orphanage, most likly because he was Raines son, and Ellone seen her as a mother figure.
somewhere in the tutorial it says that Rinoas parents are Julia and Caraway, so she isn't related to Squall, it's just neat that his father and her mother had a thing for eachother before either Rinoa or Squall were born. Kiros once said that Squall looked more like his mother, than his father, and Laguna says that Ellone told him somthing about Squall, but says he will tell Squall after the battle with Ultimecia. the theory was stated in the game, in the tutorial where it gives you some information about all the places, and characters as you meet them. thats where i found out that Laguna and Raine are Squalls parents.