How can I get rid of musty smell coming from central heat/ac vents?

Use a dehumidifier and place buckets of damp rid

You can have your vents cleaned by an HVAC company. You might have moisture in there for some reason.

When was the last service on the system? I would call and make an appointment. I service mine twice a year, spring before the ac season, and fall before heating season. A regular service contract is not that expensive. When have you changed the filters last, or cleaned them. I change my filter once you month. Here are some troubleshooting tips.

https://hayscoolingandheating.com/central-air-conditioner-smells-musty/

https://www.dynamicairservices.com/blog/why-does-my-ac-smell-like-mildew

Sounds to me like you have water problems in the basement.

sounds like you need to run a dehumidifier.

Get the System cleaned out and checked out!