All of those AIs are actually from the original Alpha which is Church. The normal AIs are separated from Alpha by force. The name 'Church' is actually the name of the creater of Alpha, Dr. Leanord Church. I guess Alpha adopted the name as his own. For Church's body, well...I think it's actually a dead body since Tucker once said that Church smells like a dead guy I think. Even though Wash says Church is Alpha, Church still maintains his thought of him as a ghost not an A.I.
What happened to Church when the EMP went off you ask? My guess is he survived. The Alpha is destroyed (I think) but his memory, the Epsilon is still OK which means Church is not destroyed completely. Other then the Epsilon, there is other AIs still OK which is in the head of The Meta. I think there's like 8 in The Meta's head. Oh, by the way, Church is replaced by Epsilon-Church who is having sudden flashes of his past and I think have a grudge against Wash (I haven't been watching RVB for a few months).
The AIs that I know of that is still ok is the Omega/O'Malley, Gamma/Gary, Delta, Epsilon and Theta.