Axe Armors are just as everyone above mentioned. They are nothing more then animate suits of steel via Dracula's magic. As for the 'Old Axe Armor' from PoR, there is a story behind that particular playable character.
From the Castlevania Wiki:
There is considerable amount of debate and confusion over the Old Axe Armor's gender and identity. The character appears to have a male voice (Jonathan's), however, the game treats the character as if they were female (Zacchino presents the armor with a rose instead of a sword and Astarte's charm attack has no effect). Artwork, which may be official or simply fan service, found on the official Konami web page depicts an unknown female warrior wearing the armor.
The description of the enemy indicates that it is a "veteran zombie" which is wearing the suit of armor. This suggests that the playable character may be a zombie, but it could be someone else wearing the armor in the playable mode. When the Axe Armor gets on the high score board of Boss Rush Mode, two portraits are listed, one showing the Axe Armor with its helmet down, and an image of Maria Renard is shown as its partner. Also, the portrait shown in the end credits is Maria's. This suggests that Maria is the one who is wearing the armor. The artwork found on Konami's web site does not resemble Maria, however.
One possible explanation for this is that like all other modes in the game, this mode can be considered a two-character mode. One character is the armor itself and accounts for the male voice in the game. The other character is the one wearing the armor, who is female and accounts for enemies' behavior towards her. This may have been the intention for this character, but they did not want to spend any additional time on this bonus mode than they had to, so they took a shortcut and used Jonathan's voice for the male sounding armor and Maria's portrait to represent the female wearing the armor. Then after the game was created, they put up artwork of what the character is supposed to look like on their web site.
The true nature of the Axe Armor may never be known for certain without an official statement and may not be important, as the mode is non-canon to the series and has no storyline.
http://images.wikia.com/castlevania/images/b/b3/Por_pic_41.jpg