If you do not have any mechanical aptitude background, I would say you have your work cut out for yourself. I would recommend absorbing anything and everything mechanical from the ASVAB book you have. After that, get another ASVAB book and do the same. And then get another book such as the ARCO's Mechanical and Spatial Relations and go through that. The library can help alot.
The math section will consist of three sections: conversions, simple algebra and word problems. That means you will be using your addition, subtraction, multiplication and division skills in great quantities and in minimal time.
The EEI practice tests are the same format as the real test, however the real test questions are more difficult. Your right, dont rely on that alone. Again, I dont know what your background is but judging from the practice tests, work on your weak areas.