2001 Explorer jolt at speed

so you have problems with the 4 Wheel Drive and also with the ABS System?

you need a local auto electrician to use a pro grade scan tool computer to diagnose. It take about 30 minutes and cuts out all the guesswork.

https://www.google.com/search?q=auto+electrician+near+me

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your post I GUESS, means the whole car works great end to end and engine runs but the transmission fails. as most do now 1998
me playing fast and loose with century.
no miles on car told (odometer)
but most are bad this old for 100 reasons inside it
A/T boxes love to fail that is there THING.
but we check fuses.
and scan the PCM/TCM.
it must be scanned. (OBD2 tool) or as the service manual tells you you how to do that 1996 to 2000 cars some have flash codes
only for the transmission (USA car)
Gen 2 Explorer
the wiki list gen 2 boxes
as you can see there are 3 boxes used that
USA cars only
5-speed M5OD-R1 manual (4.0 L OHV)<<< NO !
5-speed M5OD-R1HD (2001-2003 Explorer Sport)
4-speed 4R55E automatic (4.0 L 1995-1996)
4-speed 4R70W automatic (V8 models) (special ratios)
5-speed 5R55E automatic (4.0 L 1997-2001)

so as you can see the engine dictates the box and not told.
and the 55E is TCM electronics controlled
same with 70w
so must be scanned or guess 100 times or more.

Check your tires for busted belts in tread! you will notice a bubble in the tread if the belts have come apart! Next check your lugnuts to insure they are tight! If they are, next you should check for warped rotors (Disc brake)! With the description of a wobble at any speed, sounds more like bad tires though!!!

No.
The speed sensor just measures road speed.
Is the check engine light on ?

does the same thing in my 01 expedition, they are famous for it. you (we) will eventually have to replace the switch in it, sounds like urs might be on its last leg!

does the shake come and go at different speeds? check your tie rod ends by lifting the front wheels off the ground and grab the tire and shake from left to right. if they are tight you probbably need to replace the rotors

have the car scanned for the codes,then get back to me,most big chain parts stores will do this for no charge

check the idle control valve they sometimes get dirty

What I would do is look around the edges of the windshield where the molding trim runs along for an open gap. The molding trim should be flat against the windshield as possible. A open gap would cause a whistle type of noise during high speeds. An automotive supply store should carry a glue for hold the trim piece back down on to the windshield.

time for sparkplug change, gas filter change