Postdoc job market in relation with PhD topic
Everything in academia (as most things) becomes more and more competitive. You are facing economic pressures of course. Some academic fields draw a lot of interest because the problems there are seen as useful to solve. 

However, I worry that you are chasing a job - any job - rather than a profession. I'd advise you to think about how you want to spend your life  rather than the next job. The economics and the "trendy jobs" are bound to change and it is difficult or impossible to predict what will be "hot" next year. 

As to your statistics question, it is relatively easy to learn provided you have an adequate maths background. There are a lot of books. You need at least a bit of the underlying theory (including probability) so that you understand the principles. You also need a grounding in how statistics are applied in scientific endeavors (experiment design). But there are, as I said, plenty of books for that. You needn't try to pursue another degree or anything like that. It is the knowledge you need, not some certification. 

Finally, yes, your topic affects your job prospects in the short term. However, no one should choose a topic based on what is hot today since it may be lukewarm or cold by the time you finish. Find something satisfying to do and then find a way to do it. But keep some flexibility in your plans so that if you fall into a poor job market for your skills you have other skills you can apply. 

I graduated into a very poor job market in mathematics. I quickly taught myself computer programming and later computer science. I had a very successful career after a slow start. 



Self study in statistics is normally sufficient to use statistics for other things. I don't imply it is sufficient (necessarily) to do research in statistics itself.