Are Oracles Associative?
As Venkat told in comments, it seems hard to understand your definition for oracle which aren't defined as some machine characterisation.

Let $A^{(B^C)}$ would be the set of TM in $A$ with an oracle which is a machine in ($B$ with an oracle in a machine in $C$). It is obvious that a machine in $A$ can call $C$: it just calls the machine in $B$ and asks it to carry the message directly to $C$.

I guess ${(A^B)}^C$ would be a machine in $A$ that can call an oracle in $C$ or an oracle which is (a machine in $B$ that can call a machine in $C$) so it's exactly the same definition.

Finally, you may want $A^{B,C}$, which is certainly different from the other two (just take $B=C=NP$ and $A=P$, then $A^{B,C}=NP\cup coNP$ whereas $A^{(B^C)}=\Sigma_2^P\cup\Pi_2^p$.