P0708 means you have to repair or replace the transmission range switch. It's located on the trans axle, underneath the air compartment (air filter).
Disconnect TR switch connector. Inspect connector for damaged pins, corrosion and loose wires. Repair as necessary. Spray both sides of the connectors with WD40 and reconnect. If that doesn't work, then you need to replace the switch.
P1131 means the fuel system is stuck lean and the O2 sensor is not switching. This could be caused by a vacuum leak. Any vacuum or air leaks can cause P1131. First thing to do is replace the PCV valve as these clog easily after many miles. Just pull it out of the valve cover and push a new one in. Quick and easy. Next, check all the vacuum hoses running into the intake manifold for cracks and loose connections. Next, check the connectors to the O2 sensors and spray them with WD40 to clean and dry the connectors. Finally, spray starter fluid around the base of the IM to see if you have a leaking IM gasket. If the engine surges at idle as you spray around the base, you have a leak.
The jerking is related to the transmission problem. Once you resolve the switch issue, the jerking should go away. As I mentioned, simply cleaning the switch connector may fix it, but in the worst case you'll need to replace the switch.
Next step would be to change the transmission fluid and filter. How does the fluid look? It should be clear cherry red in color and at the right level with the engine warm, running and in park. I suspect you have either a clogged valve problem or a sticking clutch pack. If so, you should first do the simplest and easiest thing and run some Seafoam Trans Tune in the transmission for a few days and then flush the old ATF fluid and replace the fluid and filter. The Seafoam will clean out the varnish or gunk that may be causing the valve or clutch pack to stick. Try replacing the old ATF with a compatible synthetic ATF fluid like Mobil1 or Redline as they are a bit slippery than the regular ATF Fluid and will further help clean deposits out. Remember that just like oil changes, the transmission fluid should be changed every 30K miles or every 2 years, whichever comes first! Good luck and let me know if you have any follow up questions!