Stinky china cabinet -- any suggestions?  

Did it come
from a smoker's house? Easy way to tell: spray a shelf liberally with Windex. Wipe with a paper towel. If the there's brown gook on the towel, you will need to wash the entire thing with soap and water.

Onion
is a good deodoriser.
cut a large onion in half (not a red one)
and leave it in the cupboard overnight

No smoking. Onion!?!?
If I put an onion in it, won't it just smell like onion and unidentified stink?
I don't think it's from smoking. Actually, it was very clean.
It was in a basement when we got it, but the bottom piece is fine with just a hint of smell. We bought a buffet from the same people, and it's fine.
I wonder if the original owner lined the shelves with plastic. I don't know why the inside of a china cabinet would have plasticy protection -- it's not dusty or heavily used. But my second china doesn't have the plastic-coated shelves.

What does it smell like?
Chemicals? or food? or something else?

Speaking of smells... ...
Speaking of smells...
Homes or any enclosed space that were occupied by meth addicts and dealers are toxic. The fumes seep onto and into just about anything in that space rendering them toxic as well. People can get seriously ill. I'm sure it's a rare occurance, but buyers should be cautious. Much like when potentially buying an upholstered piece, you don't want fleas or bedbugs. Ask questions, observe owners... Most collectors are quite clean. No need for paranoia, just good judgement.

Chemical, with an edge of must
I don't have a good sense of smell, but I would call it a chemical smell. I was picking at the plastic shelf covering, and it would come off, but it would leave my shelves tacky and probably damage them.
Or maybe the top piece was sitting on the floor and got a little water damage.
Good tips, WoofWoof! May I add, try to not buy from meth houses. 🙂
My sellers were a very nice, middle-aged couple who had downsized from a bigger house. Then she became ill and none of their kids wanted the dining room furniture. She sold us the full-size china cabinet and base and the buffet for $75, because she wanted it to go to a good home.
We got the smaller one last month and DH thought we might be shot at while picking it up. He's paranoid, though.

Put
a heavy layer of fresh coffee grounds in a pie tin, and toast them in a broiler until they're almost burnt. Let the pie tin cool, then put it in the cabinet and shut the doors. Leave it overnight, at least.
Worked in my Beetle, after I took some bad seafood in a trash barrel to the dump. . .

Onion
like I said, is a deodoriser..it won't make it smell of oinion.
It works- give it a try !

I once went on holiday to...
I once went on holiday to come back to a broken fidge freezer with rotten fish inside.
You can buy deodourising cartridges which I think are just made from carbon, if you cant find these You could try the classic odur eaters they sell for shoes, that might work.

Charcoal Briquettes
I have used BBQ briquettes in cupboards and refrigerators that have smells or moisture problems. It works. You may have to change them daily for a while. Also, the china cabinet did not have any plastic on the shelves in the original Brasilia. The only piece that had plastic was the serving cart and that top was creme colored so you could tell. I would try sanding or some other method of removal of the plastic first.

Thank you!
I have plenty of things to try. Thanks, all!