I have striven harder to study because of the exam. I strove harder to study because of the exam. I think you mean: I have reviewed English recently for the examination. You would not 'revise' English, since that would mean changing the English language.

The past participle of “strive” is either ‘strived”or “striven.’’ I think “have strived’’ might be more common that “have striven.” In the US we use the term “review” to mean study the lesson again. In areas of British influence, the term “revise” is used, rather than “review.” (我年轻的时候在香港大学学过中文。那是第一次我听过revise my lessons.) As to the word order, using you own words I would say: I have strived (or striven) to study harder because of the exam. I have lately revised my English for the examination. In everyday American English, however, I would say something like: I made an effort to study harder because of the exam. I recently reviewed my English lessons for the exam.

It must be either "I strove" or "I have striven". The verb is similar to drive/drove/driven (a car). The meaning of your second sentence is unclear.