Re the smoky closet--maybe she worked in a place that was smoky and it got into her coats----
I would wash the closets with vinegar water and if that doesn't help, reapint them (all surfaces) starting with Kilz as you primer.
I used scented soaps and cups of charcoal in a musty-smelling linen closet. Probably should have repainted.
Re washer--can you move them and check the floor underneath? floor could be rotting/mildewed from water not draining properly. Also, check if there is any kind of filter that needs to be removed or cleaned. Clean from the back of the washer too, as far in as you can get.
Sniff inside the standpipe, or wherever it drains into-- maybe the smell is there?
Our house stank even after we threw out carpets that had cat/dog pee/poop on them,and after some repainting and re-papering. Found out our washer drained directly into the crawlspace (water was not piped into septic tank). Our kitchen sink went straight in to ground (also not piped to septic). When these things were fixed it was amazing the improvement we got!
Get a dehumidifier.
Good luck!
K. Z.