I assume that you already decided that you need to raise the roof and remove the columns to get to the porch footings underneath. If the porch is OK you may be able to lift the porch off the footings and do the repairs without having to take off the columns, etc.
Porch roofs are generally fairly light unless they are covered with slate or tile. Screw jacks are safer than hydraulic jacks but you're probably fine using a hydraulic jack of sufficient capacity if you support the roof as you go.
I would jack the roof using a 6X6. Make certain that the base of the jack is solidly supported -- if it tilts and falls then it could be dangerous (like a bomb propelled with tons of force). Also, it is good to use a thick steel plate under the jack and between the jack and the 6X6. Make certain that the 6X6 is in contact with the structure of the roof -- not just the trim.
You should have at least one helper, perhaps more.
Jack up the roof, have someone hold the nearby porch column if it is at risk of falling, and put in a 2X6 to hold up the roof. A 2X6 should be fine but it needs to be supported at the base and at the top to make certain that it does not get knocked out of place during construction.
Do this all the way around the porch until the roof is supported and you can remove all the porch columns.
Then you can attack the porch and put in new footings and wood where needed.
Rebuild the porch and level it to the correct level and slope that you want, considering the height of the existing columns. Install the columns plumb and level with each other and lower the roof onto the columns. Attach the columns to the roof and make certain that everything is the way you want it. You can do further minor adjustments with a jack and shims.
You can repair some porches in sections so you don't have to remove all columns at the same time, but this is a lot of extra trouble.
Make certain that the roof is well-supported throughout the rebuiding process.
Also, make certain that you fix whatever caused the settling and rebuild everything with water problems and rot in mind. These are the enemies of porches and small differences in construction methods and flashing/caulking can result in huge differences in how well your porch weathers the elements.