Why I am unable to focus at all while using ND filters

When you add ND filter you decrease the amount of light a lot. And for focusing you need fair amount of light and contrast. So the solution is to focus w/o filter, switch to manual focus and then put the filter to the lens.

An ND (Neutral Density) filter blocks some light and pass some light. Its color is gray, so it works evenly on all colors. However, way ND filters are labeled can be confusing. Allow me to explain:

In photography, we choose the f-stop as the increment of exposure change. We apply f-stop adjustments when we or camera automation changes the size of the entry opening of the camera lens. This is accomplished using a mechanical devise that expands or contracts the diameter of the entry pupil of the lens. This mechanism mimics the action of the human eye.

In the human eye, the pupil is surrounded by a pigmented (colored) portion called the iris after the Greek goddess of the rainbow. In the camera, we name this apparatus the iris diaphragm. Years ago it was decided that the increment of exposure was best served it doubled or halved the amount of light able to traverse the lens. Hens the f-stop adjustment is a 2X incremental change. When closing down the iris of your camera you are likely to say, I just made a 1 or a 2 f-stop change.

As the number of f-stop changes progresses, the amount of light reduction becomes exceedingly grate. Suppose you are photographing an object illumined by a 1000 watt lamp. Imposing a 1 stop filter cuts the effective lamp brilliance in half to 500 watts. A 2 stop ND cuts the 1000 watt lamp to 250 watts.

Take a look at this table that details the effect of a 1000 watt lamp:

1 stop = 500 watts

2 stops = 250 watts

3 stops = 125 watts

4 stops = 60 watts

5 stops = 30 watts

6 stops = 15 watts

7 stops = 8 watts

8 stops = 4 watts

9 stops = 2 watts

10 stops = 1 watt

So if you impose an 8 stop ND and the effective output of a 1000 watt lamp is only 4 watts. Impose a 10 stop ND and the 1000 watt lamp’s output is 1 watt.

With strong ND's like 8 or 10, the exploring light level is incredibly dim.

Camera focusing systems have a "Focusing brightness range" (Canon parlance), "detection range" (Nikon parlance) specification. This is found in the specifications section in your manual. Your camera is rated for 0-18EV for the center focus point, 1-18EV for the other focus points. Adding an ND filter will reduce the scene brightness below the threshold for reliable autofocus.

The usual solution is to lock focus with the filter off, add the filter and take the shot.

From the question:

Whenever I try to focus, it allows me to only reach to a point where the subjects are only slightly blurry and beyond that it again goes out of focus.

From comments by the OP:

Neither at auto focus nor at manual. I can feel focus alright without filters. I tried in broad daylight both using live view and viewfinder. Its like reading alphabets someone without glasses, not too blurry but yea out of focus.

and

Also, after I focus at a subject and put the filter on, ensuring no movement of focal ring, the subject appear out of focus.

If you have no problems focusing without the filters but whenever the filters are on the image seen in the viewfinder or via Live View is, at best, a little blurry that is an indication that the filters are introducing blur.

Check your filters to be sure they are clean. It can be the case that a filter looks reasonably clean because a layer of skin oil or other contaminants has been evenly spread over the entire surface. Even using a cloth that has been contaminated with skin oil can spread a layer of funk evenly over the surface of a lens or filter. Put a few drops of lens cleaning fluid on a clean cloth that does not leave lint behind and clean both sides of the filter. Does this improve the performance of the filters?

Its happening with every filter I try it with. Initially it was alright, I hardly used these filters anyway.

Perhaps it could be the case that when you previously used the filters you were just starting out and your standard of what was "blurry" and what was "focused" was a bit looser? Have you gone back and looked at some of the earlier photos you took with these filters to see if they are, indeed, as sharp as you remember them being?