Minimizing series of XORs
I don't know what sort of efficiency you are looking for, it would be good if you clarified it.
Each instruction can be described as a linear map in $\mathbb{F}_2$, so the overall
series of instructions is one linear map.
As for finding the minimal set of instructions, given a limited number of temporary variables, I believe this is analogous to the register allocation problem for compilers, which is NP-COMPLETE.