Probably, it is best to explain the difference with your own example sentence using all of the terms above:
Sie war nach wie vor in ihr Spiel vertieft.
"nach wie vor" has the meaning of 'still': She was still absorbed in her game.
Sie war immer noch in ihr Spiel vertieft.
"immer noch" has the meaning of 'still': She was still absorbed in her game. Both terms can be used interchangeably, 'nach wie vor' is more formal, 'immer noch' the more frequent term in colloquial language.
Sie war immer wieder in ihr Spiel vertieft.
"immer wieder" literally has the meaning of 'again and again': She was again and again absorbed in her game.
Sie war ständig in ihr Spiel vertieft.
"ständig" has the meaning of 'constantly' oder 'frequently': She was constantly absorbed in her game.
Sie war immerfort in ihr Spiel vertieft.
"immerfort" has the meaning of 'constantly': She was constantly absorbed in her game. Although very close to being synonyms, 'immerfort' has a stronger meaning of not stopping and going on and on with the game.
Sie war immerwährend in ihr Spiel vertieft.
"immerwährend" literally has the meaning of 'permanently': She was permanently absorbed in her game. 'immerwährend' has an even stronger meaning of not stopping.
Sie war unaufhörlich in ihr Spiel vertieft.
"unaufhörlich" literally has the meaning of 'without quitting/stopping': She was absorbed in her game without ever stopping.