Assuming it is a fence post of average height of five feet or so.
I'm obviously out of my league here men. Take this with an understanding that this is not my field. I post to stir debate/correction from knowledgeable members/and learning for myself and others who have no particular expertise in this area.
What I would do:
1. First things first. Detach harness to his chute to prevent it from manipulating his position or causing any more tearing of his tissues from lateral or rotational movement.
2. Have someone radio for immediate and urgent Evac at highest priority
3. Get another soldier to help stabilize his upper body to prevent as much movement as possible.
4. Assuming no active bleeders to clamp (probably not since object is in place), I would get two IV locks started for future pain meds/volume replacement prn.
5. Do not remove soldier from the impaled object. I would actually use ace wraps, any other material available or 100mph tape(if that’s all I had), etc to stabilize and immobilize his lower extremities to prevent movement.
6. With assistance from your teammates, have some soldier begin to cut the base of the post free from the ground. This is when you hope Reaper is with you. He can whip out one of the 1000 gucci gadgets/knives that he owns to perform the cutting quickly and without to much effort. LOL
7. With help of at least four men, lower the soldier and the post together as one unit onto the ground in a position that places as little pressure to cause movement of the object. His side on a prepositioned stretcher may be the ideal position to facilitate future loading onto a helicopter.
8. Treat for shock and manage pain based on BP/symptoms/breathing. IV Ab woudl be indicated to get the drop on the coming infections after he is stabilized. Reassure patient that James didn't make this jump and he will be fine!!

LOL
alright James, your turn to blast me for my treatment recs! haha
***edited, I seem to type to slow. James beat me to it.