If it's mold, call a mold remediation specialist.
If it's rodents or vermin, call Animal Control or another professional to remove the carcasses. If you're dealing with a foreign object, it can be as simple as removing it from your crawl space.
Now that you've determined where the odor is coming from, you can determine what action to take for how to remove crawl space smell. Moisture in the soil will pervade upward and cause your crawl space to become damp, which continues the cycle of the problem. The organic materials that makeup soil decomposes over time, and the natural process of decay invariably produces odors. Dirt can be a source of foul odors if you have a crawl space that is unsealed and has exposed dirt as the flooring. Bacteria can form where the concrete slabs have been poured and emit a foul smell. A common problem in unsealed crawl spaces, high humidity is due to the presence of moisture. Take caution and call a professional when needed. If you find visible mold, beware: molds release mycotoxins which are harmful to the human respiratory system.
If you have boxes or other items stored in your crawl space, make sure to periodically inspect them for mold - especially if you're aware of a moisture problem. Not all molds produce a foul odor, but they can cause wood rot, which creates a nasty mildewy smell. Many crawl spaces have exposed earthen floors, which can allow ground moisture to seep out from underneath your home and increase the humidity levels - especially if you don't have a dehumidifier for crawl space.
Crawl spaces tend to attract mold because of the high moisture levels. Take the time to look around your crawl space and make sure there aren't any decaying rodents, snakes, or other vermin. Is there anything in your crawl space that shouldn't be there? Do you have any paint cans lying around? What about trash that builders or contractors might have left behind, like food containers or empty soda cans? Did the previous owner leave anything? You can absolutely use your crawl space for storage, just make sure that before you put anything in there, that your crawl space is clean, sealed, and free of odors.