2001 montero sport check engine light on..neutral light flashing..doesnt shift right and jerks when you put the shifter in reverse, but does reverse ok, almost feels like it is stuck in 3rd gear..happened after i slid in reverse down an icy driveway..next day it all went away, then came back again the next night

There are a few possible reasons why your 2002 Mitsubishi Montero Sport might not go right after shifting into drive or when at a stop won't take right back off and jerks really hard when it does. Transmission problems: The transmission is responsible for transferring power from the engine to the wheels. If the transmission is faulty, it can cause a variety of problems, including difficulty shifting gears, jerking, and stalling. Clutch problems: The clutch is responsible for engaging and disengaging the transmission from the engine. If the clutch is faulty, it can cause a variety of problems, including difficulty shifting gears, jerking, and stalling. Engine problems: The engine is responsible for providing power to the transmission. If the engine is faulty, it can cause a variety of problems, including difficulty shifting gears, jerking, and stalling. Electrical problems: The electrical system is responsible for powering the various components of the vehicle, including the transmission. If the electrical system is faulty, it can cause a variety of problems, including difficulty shifting gears, jerking, and stalling. If you are experiencing these symptoms, it is important to have your vehicle diagnosed by a qualified mechanic to determine the root cause of the problem. Once the cause of the problem has been identified, the mechanic can recommend the necessary repairs. Here are some tips to help prevent these problems from happening in the future: Have your transmission serviced regularly: The transmission fluid should be changed according to the manufacturer's recommendations. Have your clutch serviced regularly: The clutch should be inspected and adjusted according to the manufacturer's recommendations. Have your engine serviced regularly: The oil and filter should be changed according to the manufacturer's recommendations. Have your electrical system checked regularly: The electrical system should be inspected for any signs of wear or damage. By following these tips, you can help to prevent transmission, clutch, engine, and electrical problems from happening in the future.

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Could be neutral safety switch.
I found a video of adjustment
https://www.youtube.com/watch?v=VcX6sI_quPU
some info on changing neutral safety switch on 2001 Montero Sport Ltd.
https://www.justanswer.com/mitsubishi/92rz4-mitsubishi-montero-sport-ltd-doug-believe-neutral.html

On the side of transmission

Range Sensor/Gear Selector/shift lever

Fix your car right away by clicking the link I attached
MITSUBISHI MONTERO SPORT SERVICE REPAIR MANUAL 1999 2000 2001 2002 DOWNLOAD

Lack of oil from the sound of it ,When checking the auto oil level start engine put handbrake on hard ,couple of bricks behind the drive wheels then drop into reverse ,now check the oil level on the autobox dipstick .If a modern vehicle with no dip stick then dealer only job to check the level

the shifter cable may have worked loose or broken. do you feel the same resistance that you used to when shifting? or just a very loose floppy shifter,if so,i suggest a broken or loose shifter cable.thank you for choosing fixya.com and by the way no relay will keep your shifter from shifting gears from park to drive,reverse.

Hi:
The shift pattern is pretty much the same on all 5 speed cars. The top row is the odd numbers, 1-3-5
the bottom row is 2-4-Reverse. The center position is neutral

Here is the key: The shifter is slightly spring-loaded to the center position. If you hold in the clutch pedal and pull the shifter to neutral, and let go of it, it will automatically be lined up in the position, that if you pushed it forward , it would go to 3rd gear, and if you pulled it back, it would go into 4th gear.
This way, to start driving, you start out in neutral, grab the shifter lightly, and push it first to the left, then forward. This is first gear, where you start out. when you want to shift to second, push in the clutch, and keeping left pressure on the shifter, pull all the way back . Here is the easy part, 2nd to 3rd. When you are ready, push in the clutch, and just push the gear shift forward , till it hits neutral, and is spring loaded to the middle. Then you just push it straight forward to 3rd, then next shift, straight back to 4th.
Last gear, 5th: push forward to the neutral row, then Push to the right till it lines up ,and forward to the 5th gear. Reverse should only be shifted into from a dead stop. Find neutral, push the shifter all the way right, then pull back towards you. Hope this helps.
Practice a bunch in the driveway!

Check the 'U' joints in the drive line. Check the engine/transmission mounts for damage or looseness. The real enigma is trying to determine if this is an engine or a chassis problem. If the check engine light is on, doing a scan of the computer should show engine problems. If no light, concentrate on anything in the chassis for periodic binding. Good luck!

i would check out the timing. but i little trick the i have learned was to put break fluid in your trany. it cleans out all junk inside