I think both grammar and usage are equally important. You can say something that is grammatically correct but makes little sense to a native speaker or may sound unusual. EXAMPLE Student: May I have a hamburger and a coke? Teacher: When is the last time anyone heard a native English speaker use "May I?" when ordering something at McDonald's? That's right, not in a long, long time. This is your homework assignment. The next time you go to Starbucks or McDonald's, I want you to listen to how people are ordering their meals, and let's talk more about it. Of course, if you don't live in an English-speaking country, then watching English-language TV can help.

Hmm, just my two cents. I find grammar generally important, but it should not be the focal point when it comes to conversation. I think the goal of communication is to be understood how you want to be understood so even if your grammar or subject-verb agreement is not that good as long as you are understood well, then that's okay. It's a different matter altogether in writing. Of course, grammar is still important in your work as an interpreter, but more important is your understanding of words (vocabulary) and context. Learning English by watching TV series/movies will be helpful especially when it comes to familiarizing yourself with colloquial English, but you need to be able to talk to people who have a firm grasp of the language. Immerse yourself in the culture. :)