What they do know about their powers is that they are caused by a relatively rare, anomalous gene. Someone with this gene can be either a Level 1, 2, or 3 anomaly. Level 3 anomalies can go through their entire lives and never be affected by the gene.
Walker and Diana Hanson are both Level 3's.
Level 2 anomalies can subconsciously use their powers throughout their lives. They have no control over this power at all. However, it is possible for a Level 2 to become a Level 1.
Level 1 anomalies know they have their powers and so can control them.
Isaac is a Level 1. He is also the strongest amongst them. His known powers are:
Telepathy - which allows him to communicate with his mind to other telepaths
Telekinesis - which allows him to move objects with his mind
Shape Shifting - which allows him to change his shape into pretty much anything he wants, including people, objects and surfaces
Force Fields - which allows him to protect himself from attacks (i.e. rocks thrown at him)
Taylor is a Level 1, but he does have a Level 2 power. His known powers are:
Telepathy - which allows him to communicate with his mind to other telepaths
Empathy - which allows him to feel the emotions of people around him, and project what he is feeling or what someone else nearby is feeling, onto another person nearby. He can also, in some cases, feel if someone is trustworthy (etc) or not.
Attraction - little is known about this Level 2 power, except that it subconsciously attracts people to him (some more so than others)
Zac is a Level 1. His known powers are:
(affinity with) Electricity - this allows him to create, manipulate and 'destroy' electricity, he is also unharmed by it.
(affinity with) Water - this allows him to create, manipulate, and 'destroy' water, he is also unharmed by it.
Restoration - allows him to restore the previous state of certain things that are not living, full list undefined.
Jessica, Avery, Mackie, Zoe and Taylor's girlfriend Rachel are currently all Level 2's. Their powers have not been fully triggered, but Rachel, Mackie and Zoe have been identified as Telepaths.