(All the suggested products are genuinely recommended based on experience. None of the products mentioned are sponsored or affiliate links.)
Lingering odors can happen for a variety of reasons: not letting clothes dry completely before storing them, clothing sitting unused for too long in high humidity, built-up residue or sometimes a washing machine that simply needs some maintenance (cleaning out the door seal and filter a few times per year should do the trick).
For general everyday odors (like smoke or tobacco) spray a bit of Sanytol Textile Disinfectant Deodorizer and leave the piece hanging to dry before wearing it. This won't remove the smell completely, but it can help reduce it if you plan to rewear clothing before washing it.
For musty odors, fill a small tub with a mix of warm water and half a cup of white vinegar, submerge the clothing and let it sit for about an hour before washing it. You may need to repeat this process a few times if the smell is stubborn. Synthetic fibers tend to retain body odor more easily over time and throughout the day, so doing this consistently before washes can help keep odors to a minimum in those cases.
