The moral aspect of Sartre's existentialism, as I understand it:
Existence precedes essence. There is no 'human nature': man is what he wills himself to be. There are no ends or goals that he is constrained to look up to. God does not exist and therefore no moral rule or code can legitimize itself by the fact that God imposed it. Even if God existed and imposed these moral rules, men would still be able to challenge them, just like the rules of any political authority. In his existential freedom man can always ask God "Why should I obey?". No authority can legitimize any moral code of conduct, nothing can make it binding on us. In the absence of objective moral rules, no action is ever impermissible, and neither is an action ever justified.
Ethics is like art. Our responses to specific moral situations are creative acts that we are forced to invent by our free choice. We cannot judge these choices to be morally right or wrong (because there is no objective morality) but we can judge these choices, just like we can judge an artist's work despite that there is no objective aesthetics. We can judge whether these choices are based on error or truth (logical judgement), and we can judge whether people are guilty of self-deception (mauvaise foi) and dishonesty towards their own freedom by excusing their actions as a result of human passion, fate or determinism, and not the result of their own choice.
Everything is permitted, but not everything is beyond judgement.