Who is held liable for damage costs if I unknowingly let a underage child drive my car and he totaled it ?

You and the child's guardian are both responsible: he is responsible because the child intentionally committed a wrongful act (or acts, rather)--lying to you about his ability to drive; driving you car when he did not know how to and legally could not. But you are responsible because you negligently, or carelssly, let an unqualified, underaged drive drive your car (e.g. you could--and should--have verified he had a permit). 
Yours is a comparative negligence state. That means that the negligence of the person who suffered a loss (you) proportionately reduces what you could get if you were to sue. For example, say that a court, unable to exactly apportion the degree of fault between you on the one hand and the child and his guardian on the other, splits fault down the middle: 50% each. If the value of your car at the time it was totalled was $10,000 and you were to sue, in this hypothetical, you'd only get half that, or $5,000, due to your 50% fault. 
So based on what you write, the child & his guardian are liable, but because you are also at fault, they most likely would not have to pay anything like the full damages. It would be ideal and you and they could settle for some amount you could both live with, they understanding that they will have to pay something, but you accepting that you will have to absorb some of the loss yourself.