As for actual members of the Cullen family, I'll be going by memory here so it may not be perfect, (it has been years since i read that atrocity to literature.)
All these characters have all the basic sparkle vamp powers from my last post.
Carlisle- the 'father,' a doctor of medicine, very high discipline, power of compassion or something.
Esme- his wife, very pointless character, has power of niceness?
Edward- stalker of bella, can read minds.
Jasper- low discipline, excellent physical combat skill, can incite or calm emotion in others.
Alice- Jasper's wife, can see all possible futures branching off of every choice. perhaps the only character who even came close to interesting, (not saying much.)
Rosealie?- or possibly rosemary I can't remember. May or may not have had a power, disliked the author avatar bella and so we the audience are supposed to dislike her. Is pro life, and that's about it.
Bella Swan Cullen- The most infamous Mary Sue, author avatar in the history of modern literature, Is stalked and emotionally abused by Edward and therefore marries him right out of high school, after she stops trying to kill herself so he will pay attention to her. Manipulative and cunning with a high deceit skill, she is physically the most powerful of the family with all her powers at the mythic level. and she is entirely immune to all psychic magic and can make anyone nearby her equally immune. Should be used as a final boss. (as the nostalgia critic put it, she would have made a great Shakespearean villain if her psychotic mindset were something the author had intended.)
There is also the werewolf Jacob who she strings along for awhile with powers similar to dresden verse werewolves only with most physical powers at the supernatural level minimum, toughness would be at inhuman. At the end his werewolfness makes him fall madly in love with an infant dhampir followed by a suspiciously repeated denial by all the characters that the is anything pedophilic or wrong about this.
All and all, a crime against literature. A nice slaughter is just what they need. I recommend hunting them down one by one. Getting progressively more challenging. Start with Esme and Rosalie and end with Jasper, Alice, and finally Bella.