I just made it back to my office after interviewing between 25-30 people at Chicago for our junior tenure-track AP position. I was in your shoes exactly 1 year ago and I joined my department just last August 2016. I was put in the recruiting committee to help build up my service.
About 50% of those we interviewed were foreign-born Asians (Chinese and Korean mainly) and very few exceptions there were really serious communication skills. Thick accents, lack of assertiveness, bowing, etc. Some of the JMP were really good, but these communication limitations are really affecting your chances in the Academic market.
My rant is how could you have spent 5 - 8 years (some did MAs before being accepted into their Ph.D. programs) in the US and never learned to communicate. Never learned the culture, customs, etc. We just finished our shortlist and only 2 out of the 10 people we are submitting to our 'fair hiring practices' committee for approval are Asians (and not in the top-4 we'll be flying in the next couple of weeks). This is not being racist or xenophobe. You really need to make an effort to integrate and learn the language!