Your problem is not unusual crawlspaces are the number one cause of poor indoor air quality. As much as 40% of the breathing air in your living space comes from the crawlspace.Solving any water intrusion problems is the number one thing to do.
If you have a musty smell then cleaning the joist, sub-floor and walls will be necessary. Use a good disenfectant such as NAS 12. (Can purchace on line, it is also non toxic)
If you live in an area of California that has low humidity then venting the crawlspace is a good idea. A vapor barrier is a must. 6-mil poly plastic is the minimum thickness you should use. Make sure that you secure it at the walls with spikes (large fender washers will hold the plastic) or bricks, tape the seams. You will need to check the current codes, most codes require a vented crawlspace with a vapor barrier to have 1 sq foot of vent opening per each 150 sq ft of space. I find that a power vent(s) attached to a humidistat is almost a necessity to provide for proper air flow. Insulating the floor joist may also be necessary.
If you live in an area where the humidity is high in summer and varies in the winter months, then venting a crawlspace is not a good idea. Bringing the crawlspace into the building envelope, sealing any vents and conditioning the space is the answer. Please check out basement systems website they explain the process much better then I can write it.