Best micro/macroeconomics books
Although this question will be flagged and closed I assume, I would recommend getting a variety of texts. Mankiw has a good intermediate macro book, that can get you from zero to a foundation, however his introductory book isn't as good.

For econometrics, Woolridge gives a good bang for your buck, but I like Gujarati's basic econometrics as well. For time series, Enders' "Applied econometric time series" is my bible.

For micro I'm not as sure, I didn't have any great experiences with introductory texts. I can't really give a good opinion on the intermediate level either, as I've only used Varian's. 

Once you get an idea of the concepts the best thing to do is to delve right into academic journals, so that you can start learning how to read them. Just that skill will help you be able to catch up fast.

I assume you're already strong in linear algebra and your other math, and some of your engineering will carry over to economics, especially your ability to think about minimizing and maximizing. 

Good luck!