What are my prospects to get a Postdoc position with just 1 publication from PhD? I am a PhD in Mechanical Engineering. I have already completed my 5 years, am writing my thesis and will be submitting my thesis in 4 months. I have published 1 paper till now. That was 2 years ago. Till then, I have completed 3 more manuscripts, but my supervisor does not have the time to go through them and approve them. As a result, I have manuscripts around 2 years old waiting to get submitted and published.

My supervisor is great with meetings, guidance and advice, but she is frustrating me with her lethargy in correcting my manuscripts. This has made me very anxious about my future. My work is quite different than what is being published at the moment in my field. So, I think my manuscripts would still find a place in a reputed journal in my area of research. However, I can't be very sure of that until I actually submit the drafts. Also, I can't just go behind her back and submit the manuscripts as I don't want to sour my relationship with her.

I am not able to apply for a postdoc position as I am sure that I won't get any response without having any published works. I will be submitting my thesis by end of June. I will defend this fall. But, I don't know what I will do next.

I have applied to various industry positions and have got rejections. I don't think that I will land any position soon.

My question is, what are my career prospects at the moment? And what would the best course of action for me at the moment? 

I am almost 30, been in school for Masters and PhD for the past decade. I am feeling quite hopeless. Ideally, I would like to stay in academia as I love doing research and teaching. But, I find that future dissolving away in uncertainty.
Except for the difficulties in getting your advisor to respond to you, nothing you say seems unusual. Even that is too common, though. But your age, etc. is pretty typical, or at least not far outside the norm. 

But I think that if you can unblock the block that you will be in good shape career wise. Your difficulties with industry could be a lot of unrelated things, and you haven't really tested yourself yet in the academic marketplace. 

If you want a career in academia, I suggest you start a search, either as a post-doc or a regular position. You have a lot of work-in-progress to point to which is a point in your favor. I wouldn't wait until you get the block cleared and then something submitted and accepted. It will take to long, but, I suspect, not be judged fundamentally differently than work in progress.

The only issue I see is your "out of the mainstream" research interests. You will need to find a way to present that as an advantage, not a disadvantage. As Apple used to say, Think Different. 

There is, I think, no reason to do the two things sequentially: advisor, job-search. Work on both in parallel. 

On the advisor front, however, you might want to make it more incremental. Rather than "all these papers", focus on getting just one out the door and then repeat as needed.