"Is anybody hurt?" means is anybody hurting right now.
"Has anybody been hurt?" means did anybody already get hurt.
Technically, you could ask them both in the same situation. Eg. if you hear a huge crash in another room, you might run in and ask either of those questions and it would be considered appropriate.
However, I think you would be more likely to ask "is anybody hurt?" when you are in the situation yourself (as the above example), and "has anybody been hurt?" when you weren't there for the event or after the event is over. Eg. if there was a strong storm somewhere and you heard about it, you might ask "has anybody been hurt?"