When in 2 wheel drive and accelerating, the car pulls to the right, upon decelerating, it goes left, it would seem to me that I have 3 wheel drive, with the rear nearside wheel still driving. What is the solution please.

Sounds like a loose wheel, check them ,

It could be a wheel bearing either the left or right side maybe both. When driving around corners note if the noise gets louder when turning either way, for example if the noise gets louder turning right then the left front wheel bearing is the problem, the same for turning left, the right front bearing would be the problem. If the noise stays the same and changing on acceleration or deceleration the problem may be more serious, possible a final drive issue like a bad pinion bearing ring and pinion gears.

Hello,

If problem only occurs 'under power' sounds like a u-joint (driveline - rear wheel drive) or a cv-axle (front wheel drive). Check for excessive play, fluid, boot tear and breakage.

Shakes? Not very specific. It could be a loose wheel, wheel out of balance, the balance weights may have come off one or more wheel rims (check for the marks on the rims inner and outer rim where they used to be).
As 1996 model, it could also be worn out suspension bushes.
If you drive on a straight road, and you change from accelerating, to decelerating, does the car skew (turn left or right slightly), this would indicate worn suspension bushes at the rear, acceleration pushes the rear axle forward, deceleration pulls it back, if there is wear (slop) in the rubber bushes, the changing alignment of the rear axle causes the car to "throttle steer". At cruise, this could potentially set up a sort of harmonic motion, and cause a form of "shaking".

Bearing problems in the manual trannies is common, tear it down and rebuild it.

here are some common causes and solutions to your problem.

1. wheel alignment. go to your nearest tire service center and have your wheel alignment and wheel camber checked.
2. Tire pressure. perhaps the tire pressure in your left tire is much lower than the pressure on the right tires.
3. if your vehicle is a rear wheel drive vehicle, although very uncommon, the problem can be on the differential. differential is the device that makes the movements on your wheels syncronized even during on turns.

Your car needs a front wheel alighnment.When it pulls under acceleration and then goes the other way,get an alighnment.Torque pulls the wheels one way and then the travelling pulls it the other.Hope this helps

Loss of fuel pressure.
1. Clogged fuel filter (replace anyway)
2. Fuel pressure regulator (stays open)
3. Fuel pump

a arm bushings worn out

bearings make growling noises and axles cv joints make a flutter vibration when accelerating or decelerating