How can I get rid of old furniture smell?

Wipe it with white vinegar. Do the inside and outside.

setting the pieces in hot sunshine will also help.

Cedarwood oil. I've used it for fifty years.

The vinegar trick also works for tobacco smells. I had old books that smelled of mold and cigarettes. I saturated a sponge with white vinegar and placed it in a small saucer. I then fanned the book pages and stood them up on edge around the saucer. I placed a large cardboard box over them and just left it alone for about a week. What a difference!

I use orange oil based furniture polish. It replenishes the moisture in old wood and leaves a fresh citrus smell.