Is a single string enough to prove regular expressions inequivalent?
Does it suffice to show that a single string is not present in the language and hence its different from the rest? 


Yes. It's actually a very neat proof.

Formally speaking, you have found $w \in \{a,b\}^*$ with $w \in L_1$ but $w \not\in L_2,L_3,L_4$. That is sufficient to show that $L_1 \neq L_2$, $L_1 \neq L_3$ and $L_1 \neq L_4$.

You have not shown that $L_2 = L_3 = L_4$. The phrasing of the question seems to suggest as much (MC questions are boring!) but you may want to prove that as an additional exercise.


   Hint: Translate into NFA, determinize, minimize, check for isomorphy.