I found a semi-old couch that my university that was going to thrown out. I snagged it before they could throw it in the dumpster. It is a really nice couch that I could really use, but it has a slight mildew and dusty smell to it.
Sprinkle baking soda all over it. Leave for a few days and then vacuum it up. If that doesn't work, try cat litter. Both absorb odors.
You could hire a steam cleaner. Or you could buy a bottle of upholstery cleaner and follow the directions. You might want to air it as much as possible by taking the cushions off and leaving the windows open as much as you can, that will help.
Use an upholstery cleaner, or a rented carpet cleaner with attachments for furniture. Put straight white vinegar in the clean water tank. The vinegar odor wont last long. It's amazing. Then just for good measure, use fabric spray, like Fresh Care. Use fans to dry it. Be generous with the vinegar, but make sure you suction most of it out.
The best deodorizer of them all for sure is our lucky old sun! Yep, fair dinkum, it takes time but works every time.
This is a page about removing musty smell from leather furniture. Mold and mildew can leave your leather furniture smelling musty.
I just bought a foam filled leatherette suite. It has a damp smell. There is no way I can open and clean the interior.