I hold OCI and US citizenship. I live in India. Should I do llb in India and LLm abroad. If I do llm abroad, can I practice there?

If you do your LLB from here, then you will either have to clear the foreign jurisdiction's equivalent of the Bar Exam that may further require certain years of experience or an LLB equivalent degree, depending on the jurisdiction. Only then can you practise there. LLM is not relevant in this context.