Editor rejected my paper stating that reviewers had refused to review it long after submission; How can I understand what is wrong with my paper? I am having very  frustrated at the turn of events and review process. I had sent a paper to an International Journal. The paper was based on my work and well received by PhD committee of my Institute. The paper was submitted 3 years back. The paper was in status "Editor Assigned" for 6 months. After that its status changed to "Under Review". After 9 months in this status (15 months after submission date), I sent a polite mail to editor asking about how much time it will take to complete review? There was no response. After I month similar gentle mail was sent. There was no response. After month, I again sent query (18 months after submission). At that Editor replied saying that they could not review the paper as assigned reviewers either refuse to review or did not agree to review. The paper was rejected after 18 months without any review comment.

So how does one know where it requires improvement? If paper was not of required quality why they kept with them for so long?  

I feel that it is wrongly rejected.  

Is it correct answer?  

How can it show status as Under Review and then Editor says no Reviewer did not accept or refuse. My understanding is that paper goes in "Under Review" state only after "Reviewer" accepts to review. So what would have happened? Why Editor requires 3 months just to tell the status and comes back with mail like this? Editor did not bother reply to mail. Is it that he got angry because of persistent queries. 

I had even worst experience with next Journal. The paper was submitted and it remained in status "With Editor" for 9 months. Wiser by experience, I asked Editor about status? After persisting with it for about 2 more months, Chief Editor said that they rejected paper based on quick review as paper is not suitable to Journal as it does not meet its criteria like Originality, Depth etc. Again there no review comments about improvement.

It is not sour grape, I do feel that around 60% papers in that Journal do not possess these qualities and have been published in 6-8 months (after revision).
If paper is not of required standard, they could have rejected in 2-3 months, why it took them such long time. If I would not have sent mail, probably it would have remained with them for long time. This work is now 3 years old not published anywhere and I even do not know what to do to improve. I am feeling very bad and really do not know what to do?

What would happened? Is it wrong to ask editors about status even after 9 months or year? Our University requires two Journal publication for PhD thesis submission and really do not what to do?

Many friends are suggesting that publish in Open Access Journals.
The delays you mention are really excessive (note: I feel that way even though I am a mathematician), and your anger is quite deserved for that.

From what I heard from editors I know, it can happen that a paper is sent to successive referees who decline to referee, or worse accept and then don't do the job and do not respond to queries. At some point, the editor have to either do a referee's job themselves, which usually do not happen, or reject the paper. Usually, this happen with papers that are not clearly wrong or uninteresting, but that are difficult to read and do not really interest the tentative referees. In some case, you can have better result by submitting to a different, e.g. more specialized journal.

In your case, what bothers me is that being in a PhD, you have an advisor. What does she think of the paper? If there is no obvious problem in it, did you submit to journal suggested by her? On what ground? Is it possible that your institute, whose PhD committee you says received your work well, has much lower standards than international journals?

In any case, the only effective answer to your question is: seek feedback from a knowledgeable individual. It could be your advisor, but if needed it could also be another senior researcher in your field and institute, or even someone working elsewhere in your field. The closer the better, as it increase the probability of getting the feedback and the probability that it will be honest.

Last, as already mentioned, open access journal can be as toughly selective as subscription journals, and should not be considered easy shots when everything else has failed. I would not recommend submitting to a shady journal, let alone an OA one since shady OA journal often charge several hundred of dollars for publication.