I have completed my masters in English Literature from India and now want to do my PhD from the US. Should I take both the tests, i.e. TOEFL and GRE? Or only TOEFL will be enough? And if I need to take the GRE, then is it a must to take the subject test as well?
The TOEFL and the GRE are quite different. The 'point' -- in as much as standardized tests have one -- of the TOEFL is to figure out if you have sufficient mastery of English to study (and potentially be a Teaching Assistant/Instructor) in an English-speaking environment. The TOEFL is generally required of all non-native English speakers. Graduate programs often waive this requirement if the student is enrolled in and about to complete a degree from a US institution (or did so recently). It's possible that they might waive the requirement for a similar student from a university in other English-speaking countries such as the UK, Australia/NZ, etc. but I am not sure (I don't know anyone who has tried.) Sometimes graduate programs will state that they will waive the TOEFL requirement for a student from a bachelors/masters program with English as a language of instruction. Most Indian colleges/universities I know of are English-medium, but I've never heard of an Indian student applying from India who has had the TOEFL requirement waived this way. (I am an international student from India. I was an undergraduate in the US, and the TOEFL requirement was waived for me by all the graduate programs I applied to.)
The GRE on the other hand is generally required for all applicants, domestic and international. Wikipedia says that it aims to measure ''verbal reasoning, quantitative reasoning, analytical writing, and critical thinking skills that have been acquired over a long period of time and that are not related to any specific field of study.''
The TOEFL is more of a checkbox - programs just want all their international students to have some minimal mastery of English so they can perform the usual duties of a graduate student. The GRE is more of an actual comparative tool for all the candidates which can actually affect an admission decision. The two tests are quite different in content and questions --- the TOEFL might contain a question which will play an audio clip of a 'usual' conversation between a student and a professor and ask you whether you can understand what was said; whereas GRE questions might ask you to critique the logic of an argument or perform some high-school level problem-solving task.
Notably the TOEFL obviously does not have a quantitative section whereas the GRE does.
At this point in the US, I believe there are very few graduate programs that do not require at least the general GRE of all its applicants. Subject tests are not as widely required, but in my experience the better programs require them.
tl;dr: you will probably need to take both the GRE (general) and the TOEFL. Look into the programs you want to apply to to figure out whether you should take the GRE subject test.
There is no general rule here. The only solution is to look up the requirements of each program you are interested in applying to. Some schools may require both, others the TOEFL but not the GRE, or vice versa. (As for the subject test, it will most likely be required of all applicants or not required for all students. Domestic versus international likely won't matter.)