Am I not fit for grad school if I have a bad GRE score? Should I give up? I have taken the GRE four times and got 148 Verbal, 157 Quantitative, and 3 on Writing.

By the way, English is not my first language. I am a foreigner that works in his home country. I want to do a PhD in the USA, but I can not get a descent GRE score. 

Does these results say I am not fit to do a PhD?

I can not get good reference letters. I graduated from a developing country university which has no graduate programs and Faculty works part time. I did electrical engineering.
As some answers for a similar question have pointed out regarding GRE scores, the answer could be maybe. Language too, is not necessarily a hard barrier to doing a PhD in the US, as long as the potential advisor can overlook it.

However, I would strongly urge you to find good reference letters as having both poor letters and poor scores is generally a pretty big red flag, or at the least significantly reduces the competitiveness of your application.

You may still have a chance by contacting faculty directly in less popular or lower ranked schools, which may have a shortage of applicants. This does vary on the field.