I have been reading Quran in English phonetic transliteration since a couple of years now. Is it okay to recite in this way and does it offer the same rewards as someone reading the Quran from the Arabic script?
It is ok to recite that way. After all, there have been many Muslims who can't read at all and still recite from memory.
Still there is a certain blessing that the actual Arabic script of the Qur'an is said to hold and it is narrated that looking at the Qur'an is a type of worship; my understanding is that this involves the actual Arabic letters. So it is good to learn to read the Arabic script if you can. There are a lot of self-study materials available today.
But if you can't, that is also ok too.