Northern Hewer is on the money with his insights.
Certainly cabling is good; you can also tie the beams and posts to each other with temporary hardware at critical points.
I always do a careful elevation survey of the levels for *every* post before I begin. Then I set thumbtacks in each post for the "as is now" and the "target" elevations; I periodically reset the "as is" points to monitor progress until the two coincide. Gives me a quick visual reference of where the priority points are at any given time.
Drawing a map of what is settled and exactly how much will reveal what is really going on with the barn in ways the eye alone cannot. It will give you a better sense of how to reverse and correct the larger process that caused the settling and where to logically begin relieving the stresses.
People ask "how do you know how much jacking is too much?" My answer is "I listen... Creaking is okay, Cracking is bad..."
An inch at a time, always back up your jacks with blocks and shims as you gain, and work the barn as a whole, don't try to do too much at any one point. It's educational to be merrily jacking away and hear a crash as a temporary post 40 feet away falls loose.
The barn will "want" to come back, and you'll feel it get happier as you get close to level again.
Good Luck,
Pete
