To repeat: The original receiver is legally a machine gun all by itself, whether it has the rest of the parts connected to it or not, unless it is torch-cut to BATFE specifications.
It is illegal in CA.
Even if you were not in CA, it is illegal for you to transfer on a Form 4 through a Class 3 SOT, since you are 19.
It is also illegal for the seller to own the original receiver in WA state, again unless it is torch-cut to BATFE specs.
EDIT: Searching Gunbroker,
this is the only StG-44 I'm finding, and it's neither $8k, nor semiauto, nor in WA...
EDIT II: Further, even if the gun is a parts kit built on a new semi-auto receiver, it would be illegal in CA, since it is semiauto, feeds from a detachable magazine, and has a pistol grip that protrudes conspicuously below the action.