First point, I have to disagree with the other comments, from the way I read it, you are not committing any crime.
As a side note, I find it odd that on so many answers people jump to commenting, "You could go to jail."
But who knows, maybe I am wrong and do not understand how many folks are in jail for one time title administrative errors.
Lets step back, you are the legal owner of this vehicle, I am speaking purely in terms of of the UCC definitions, not the administrative application of title. The is the system used by the state to track ownership, transfers, apply liens, manage registrations and license plates, and to protect consumers in that in general you can expect the title holder to be the legal owner, etc. But there are many vehicles that do not have titles, ie old cars, farm vehicles used on private property, even if it is a 4 door car, etc. And all those can be legally bought and sold.
And pardon me being direct, but you asked, this sounds like a mess, I am sure there is some really interesting back story, but still a mess, and I am guessing your next vehicle purchase will be more "normal". And ALWAYS get used car inspected by a mechanic, I do not care if it is a private sale or used car lot, get it inspected and if they decline, then move on to the next vehicle.
On to your question. Let me summarize the situation as I see it: you own the vehicle and never converted the title to your name.
Do you at least have a bill of sale?
Can you convert your IN title to a CA title without getting smog and registration? If so do that. They do allow out of state vehicles in the state, but there are some rules regarding that process.
Or convert the title in IN, but I am guessing that is not worth the effort.
Who is this buyer and why do they want a no-title parts car? That could be some type of scam, who knows?
You can sell the vehicle, I would require a bill of sale that clearly states you are the legal owner, but do not have a title. The car is being sold As Is for parts and the buyer will not attempt to register the vehicle or obtain a title.
List the vehicle VIN, make, model, year, color and miles. List your and buyers name and address.
Two copies, each person signs both copies and keeps one copy.. You need to see the buyers state ID and make a copy.
My advice is to sell it to a junk yard and lower your risk and be done with it.