Is a piece hanging if it is defended by a higher value piece? In this extreme examplethe c5 pawn is defended three times, though white can take the pawn with an advantage.

 [FEN "2r1k3/2r5/2q5/2p5/8/8/PPR5/KN4B1 w - - 0 1"]


What about if the defender is a higher value piece than the attackers, even though it's defended and attacked twice? Clearly, White can take the pawn with an advantage.

 [FEN "8/8/3k4/2p2q2/8/8/PPR5/KN4B1 w - - 0 1"]


Now it's not hanging:

 [FEN "8/8/3k4/2p2r2/8/8/PPR5/KN4B1 w - - 0 1"]


What do you call these type of situations if it's not hanging piece?

This position also has a hanging piece:

[FEN "2b4k/3q2pp/8/5p2/8/2B1N3/PP6/KN4Q1 w - - 0 1"]
This would still be called a hanging piece. If the piece can be taken with impunity, it is a hanging piece. It is irrelevant how many attackers there are on the piece, how many defenders there are on the piece, or the point value of the attackers/defenders.