Truth be told, it's hard to tell the details to you. But I can say I seldom use '예요'. You better use '입니다' and forget other details.

~입니다 is the most formal. ~예요 isn’t necessarily informal, it’s more of the formal language that you use everyday. You will use it with almost people you meet, unless they are someone you need to show particular respect for. The informal is ~(이)야, used only with those you are close with (ie. friends, some family, etc). There is some more nuance than this, but this is the basic idea.