Actually new books also smell, but the odor is more pleasant. Virtually everything smells to some degree because some of the molecules escape from the object into the air. The technical term for this is outgassing. If an object is kept in a tightly sealed space such as a document under glass in a frame, over time, the image of the document is discernible on the inside surface of the glass, caused by outgassing deposits.
All the previous suggestions are valid, baking soda, activated charcoal and zeolites (kitty litter) will absorb the guilty molecules, but when they are replenished by continued outgassing it will be a continuous battle. Other helpful things are lots of circulating fresh air, indirect UV light, ozone(?!), hydroxyl radicals but they all have downsides as well. So long as paper (especially acidic paper)keeps self-destructing and printing inks and glues keep breaking down and chemically changing, there will always be outgassing and that “old book” smell.
Try hanging the magazines on wire clothes hanger so the pages are somewhat fanned, fill the box with zeolites and put in a small fan inside to provide gentle air circulation. Take care not to cause a fire! Consulting a conservator is an excellent idea!
George Schwartz, ConservArt