When I ride the bike, it feels like the rear wheel is being pulled off the bike towards the right. Its more noticeable when I turn left or make any maneuver towards the left. But when I turn right, the bike feels solid and I make any maneuver towards the right with confidence. I must say that the rear shocks have been bent for sometime now also (probably before the experience).
A week ago, I checked the swing arm per the Clymers instruction and I think its ok. The shock was bend in an arc fashion with the inner facing right some time ago. Then I removed it and turned it 180 degrees horizontally so the inner arc faces left since some two weeks ago.
Might the shock be the problem?

Sounds to me like the shaft of the shock is bent and you would be lucky if the shock is working at all.
Do you know how the shock got damaged?   I would check the swingarm for being twisted. We have seen 1 person from USA that twisted one and my wife's K75 twisted it in a very low speed crash.
Put the bike on the centre stand on a solid flat surface and check the rear wheel is vertical and the way you describe the handling I would say that it would be likely to be twisted to the left at the top of the wheel.  It is quite likely the shock was damaged at the time the handling problem occured and is related to the same incident.

I welded my center stand because it got broken last year. I don't think its in original shape for accuracy. However, the wheel looks vertical, but I'll try to check swing arm again per your suggestion.
Its 12am now so will check in the morning.
thanks Rick

I checked the swing arm, I don't see it bent. 

I think it's worth noting that a "nock" sound comes from where the steering is connected to the frame when I pump the steering down and up hard with the front brakes engaged. I also hear the same sound when I brake (front) hard during riding from same location. Might it be connected to the drifting?

Another thing is that I noticed from last week that most of the weights attached to the front and back rims as balances are off. Can it also cause the drift feeling?

I also changed the front wheel and back wheel as they were badly worn.  The former ones were the factory sizes but the ones I changed to are 110/90/18 (front, but it's a rear tyre, I wasn't getting a front tyre for the rim) and 140/80/17 (back).

What can cause the shock to bend apart from accident: I don't remember an incident that should cause the swing arm to bend, and it doesn't look bent either. The only accident I've had with the bike was at least 7 months ago, and it was not serious: My front wheels got locked on a tarred road with loose sand on it near a ramp. I didn't notice the sand before breaking. The bike fell on its right about the same spot I applied the brake. 

This drift feeling started just last week.

The only thing I can think of to bend a shock is impact of some sort. Is it possible that someone in a car had bumped the bike while it was parked then picked it up and said nothing. The bumper on many cars is at the height that could impact on the shock.
The knock you describe could be loose steering head bearings. This will need a second person to help, pump the front as you were saying and feel if there is any movement between the frame where the steering stem goes through the steering head and the top and lower triple clamps. For it to have an audible knock it will be easily felt if there is movement. The change in handling from that would be most evident just as you are starting to lean into a corner and the forks change position slightly it will also cause a shudder when braking.

As for the tyre sizes many of the guys here are running those sizes without any problems.

Try to check the alignment of the wheels using a string line, you may find this easier with a second person to help.

There is the kind of shudder and movement you described when I break and the shocks change position, I notice it even pumping with the front brakes engaged. So do I change the head bearings or just do some tightening?

It's worth noting that I always have my saddle bags on, so any side impacts should affect the saddle bags first. What about high speed on a really rough and bumpy road, with a pillion? I remember a journey I made with a pillion on a very very rough and bumpy road, I did about 150-160km/h. At the end of the bumpy road, one front shock (right) Leaked badly. Could the impact from such a journey with a heavy pillion cause a bend? I have not any accident that should impact the rear shock.

Having the panniers on all the time rules out any impact from a careless driver. I imagine a heavy and sudden downward load like a big pothole could do that. Can you post a picture of the shock it would be interesting to see where and how it is bent.
With regard to the front I would be inclined to put new bearings in if you don't know when they were last changed.

Having a bent shaft on the shock could cause the suspension to be very jerky in its movement which could cause the feeling of changing direction a bit in a corner

Rick,
I didn't make time for maintenance on the bike today. But before I went out to teach this evening, I adjusted the shock to its lowest setting, and I was surprised to notice that the drifting sensation had reduced drastically and was hardly noticeable.
Could this imply the drifting was resulting from the damaged shock?
The rear wheel did touch the fender on bumpy road, but that's to be expected. However, the drifting, though present, was very minimal and hardly noticeable in most part of my 60km ride today. So what do you think??

The shock is bent so a new or good one is needed which would be my next move along with the steering head bearings. Things like that will turn the very best handling bike into a real pig to ride

Yes, that's just what I'll do. Thanks a many Rick