Some odors are harder to get rid of than others. Odors that come from organic sources---mold, food and decomposing matter---are most often sulfur-containing compounds hanging in the air or lurking in fabrics with fats or proteins. They may result from last night's fish or the swim that your dog took at the park on Sunday, but most can be neutralized with one or more simple household chemicals.
Neutralize odors by eliminating their source. Find the source of the odor by using your nose or a black light (for organic stains). When you find the location, clean it with some dish washing soap and rinse with vinegar. The soap is a surfactant and breaks down surface tension, and vinegar is a mild acid that kills bacteria. Citric acid is another neutralizer that can wipe out bad smells like fish and onions. Or choose Simple Green or other biodegradable cleaners---anything that works as a surfactant to break up the grease or fat that holds the stinky compound together.
Neutralize musty odors by removing the moisture that carries them. Invest in a dehumidifier to take the excess moisture out of the air. Then fill a nylon stocking with plain clay cat litter, dried (used) coffee grounds or crushed plain charcoal and hang it in the room. All of these substances draw moisture in. The clay is fairly passive but the coffee grounds give off a pleasant odor of their own and the charcoal actually traps the particulate matter that carries the compounds that make up odors.
Houseplants consume carbon dioxide and exhale pure oxygen. Plant aromatic herbs and enlist their help to fight odor: the same enzymes that create the pungent aromas of many herbs interact with sulfide in odors to neutralize the smells. The mint family has provided odor-fighting scents for centuries; Spearmint and Wintergreen are aggressive growers and Lemon mint is a new variety that combines citrus and mint. Plant herbs near the kitchen door and cut mint for summer teas and bouquets in the kitchen to neutralize cooking smells. Basil is another aromatic herb that gives off aromatic scents when hung in bunches or kept in vases.
Use natural chemistry; many substances that are used in the odor absorbers sold commercially are available on the grocery or hardware store shelf. Use bicarbonate of soda (baking soda) to soak up smells in the refrigerator and in smokers' ash trays. Plain white vinegar vapors interact with cigarette smoke and animal odors. Plain barbecue charcoal or aquarium charcoal set in a dish will neutralize cooking and household odors. Household cures require gentle agitation every few days and replacement every few weeks, but a little experimentation may find a simple cure. All of these substances contain chemicals that oxidize compounds in odors, meaning that they produce new (non-smelly) compounds. A scrub of peroxide, baking soda and vinegar used on materials that smell of wood smoke, for example, will produce oxygen, water and a precipitate of soda ash---and no smoky smell.
If all else fails, invest a few dollars in an odor fighter like Fabreeze, Fresh Wave or Bad Air Sponge. Most of them combine a moisture absorbent material with plant oils or chemicals to kill the odors riding on the moisture brought in by the absorbent material. Use these products only as directed on the package.