Can a large $V_\alpha$ satisfy Comparability but not be well-orderable? Say that a set satisfies Comparability if any two of its subsets are comparable: one is injectable into the other. 
Are there models of ZF containing ranks $V_\alpha$ which satisfy Comparability but are not well-orderable, where $\alpha$ is greater than an inaccessible cardinal?

Yes, this is consistent; for instance, if $A$ is an amorphous set.
An amorphous set is an infinite set which cannot be partitioned into two infinite pieces: if $A=B\sqcup C$, then either $B$ or $C$ is finite. It's easy to show that any two subsets of an amorphous set are comparable, and the existence of amorphous sets is consistent with $ZF$.

I'm not sure I understand your second question - are you asking whether there are models where $V_\alpha$ satisfies comparability for $\alpha$ greater than an inaccessible, but $V_\alpha$ is not well-orderable? Or are you asking merely whether the existence of non-well-orderable sets satisfying comparability is consistent with ZF + there is an inaccessible? 
The answer to the second question is yes; to the first, I don't know.
