@serenesurface-- That is a difficult situation.
You see, the kind of changes required to permanently improve basement air cannot be undertaken by an occupant. A ventilation system needs to be put in or the current one needs to be changed. There are also materials that should be used on the walls and floors to keep moisture and mold out. The article already mentioned these. Unless your landlord was willing to allow you to have these done and cut it from your rent payment, you can't possibly invest so much money as a renter.
The best you can probably do right now is to get a dehumidifier. These are portable, you just plug them in and they dehumidify the air. This won't be as good as a ventilation system but it should get rid of the moisture and odor a little bit. Also, if possible, keep the basement door that leads to the upstairs of the house open for more dry air.
You might also want to stop by a home improvement store and ask someone who works there for advice. There might be some cheap materials you could use to keep the moisture out without breaking the bank.