How can I level and finish a slanted deck that was enclosed?
Basically you build a new deck on top of it:



In your situation, I'd cut long triangles to use as sleepers, opposed to the shim technique shown here. Subfloor it with 3/4" plywood. Finish with your desired floor covering.

Use a table saw to rip 2x4's; having one end zero inches and the other 2". Install them directly above the existing joists, drilling pockets from the top down if needed, for screws. 

Blocking between the joists is advised. 

The finished floor will be slightly higher than the adjacent one (that's what thresholds are for), take into account the clearance for any doors that open out, onto it.

If the height discrepancy or if clearance is an issue, you're looking at having to gut the decking. This would enable you to sister to the old joists and bring it up to level, while keeping a low profile.