I'm not really sure what kind of agency you're talking about. In your question you ask about an organization that helps with "oversea education's applying." But in the body of your text, you say, "an institution provided english training service." The agency that helps with the application process would probably be called an overseas study agency/organization or a study broad agency/organization. A company that helps with your English would be called a language school.

I got a mail once from an agency which was called an "overseas training provider" but I don't know if this is the official term. I think it would be called a "study abroad agency" .