What causes old wood smell, is it bad to ignore it, and how to clean it?
If you put your clothing in there as-is, the clothing and then you, when you wear them, will smell just as bad.

The smell comes from such furniture sitting closed up for long periods of time.  I've found that taking out all the drawers, opening all the doors, and exposing all of it to fresh air and, if possible, direct sunlight, will eliminate the smells in a relatively short period of time.

If it's more stubborn, you can try an "oil soap" type cleaning product.

If there were mold and mildew, you should be able to see that on the surfaces and if present, you'll want to clean that with an appropriate commercial cleaning product that acts on mold and mildew.