Okay, let's see:
Sonny: unrelated to anyone else in PC when he came on. He as introduced when Scott Baldwin's teenage daughter from an old fling came to work his strip club. Sonny eventually took over the PC mob.
Carly: Bobbie's daughter, given up for adoption at birth. She came to PC to find Bobbie, married and divorced Sonny a billion times. They have two kids.
Carly came to town with the intentions of destroying Bobbie's life because she gave her up for adoption by stealing Tony Jones away from her (which she did) but in the process ended up having a one night stand with A.J. Quatermaine and getting pregnant by him. The "Q's" tried to claim baby Michael as their own. Carly's adoptive mother showed up in town and told Bobbie that Carly was her daughter, then the adoptive mother had a heart attack during the confrontation and died.
Jax: brought on as Mac Scorpio's friend/rival about ten years ago. He's a billionaire. He and Sonny hate each other, as they were both once in love with the same woman.
Sonny and Jax hate each other because they were both in love with Brenda Barrett, who was brought on as Julia Barrett's little sister. Julia Barrett was brought on about the time they brought on "Bill Eckert" who was really Tony Geary acting in another role. Bill Eckert took a bullett in the back protecting Lucky in a cave by.....who shot him? Does anyone remember? What was that guy's name?
Courtney: Sonny's half sister. She and Jax were married until...
Courtney married A.J. Quatermaine first, then they somehow hooked her up with Jason and they fell in love. Courtney's been with just about every single male character in Port Charles!
Nikolas: Courtney and Nikolas hooked up when C and Jax were having marital problems. Nikolas is Laura Spencer's son by one of the Cassidines (from her time locked up on their island in the old days). Nikolas came to PC to find Laura.
Stephen Cassadine, who is Nickolas' father, had an affair with Laura while Helena trapped her on their Island. They had a baby together, who is Nikolas. Stephan had been watching her life from afar (after she escaped) and knew that Luke and Laura's little girl (now a young woman--Leslie Lu--now called "LuLu") was in need of some kind of blood transfusion or some such life saving procedure that only a family member could be a donor for, yet everyone tested negative. That's when he sent Nikolas to town and voila! He was an exact match and saved LuLu's life. Ofcourse that meant that Luke would hate him forever when he found out that Laura had a Cassadine child, and it really worked on Luke and Laura's relationship for a long time because she never told him about the affair.
Emily: was Nikolas' wife when he hooked up with Courtney. She is a Quartermaine by adoption (her birth mother and Monica were in the same cancer treatment program and Monica took Em in when she was a preteen).
Sam: a con artist who came to town and hooked up with Sonny, got pregnant by him. Jason agreed to pretend to be the baby's father since Sonny was still on again/off again with Carly at the time. Sam lost the baby; she and Jason fell in love.
Alexis: Nikolas's aunt. She is Stefan and Stravros Cassidine's half sister so not a full, "evil" Cassidine.

She had a daughter by Sonny (yeah he gets around) and when the girl got sick, Sam's baby was the only person who could help (presumably b/c Sonny was the father of both). Sam's baby died.
(Now, it looks like GH is about to turn that storyline on its head. Maybe Alexis and Sam don't just have a Sonny connection...)
Anyone else, you ask? A couple of people you might not know but who have been around a while:
Lucky and LuLu: Luke's kids (Lucky is a cop)
Elizabeth: Lucky's wife, a nurse at GH
Mac Scorpio: Robert's brother, used to own a bar, now police commish
Maxie and Georgie: Mac's stepdaughters, bio daughters of Frisco and Felicia