just guessing here. using my vast MMO gaming experience and DnD lore/ knowledge base.
Thorn Crown :Christ was given the Crown before his march w/ the Cross. could it have some type of enh stamina/ endurance thing, pain suppression, damage mitigation? sort of like the Winter Mantle but not coming from the individual but the faith magic. something cleansing like also might fit. also was supposed to be a joke calling him the king of the Jews. might it also project and aura that aids/ supports allies?
Shroud of Turin : healing and resurrection I am thinking. they way I see it maybe the one previously seen is not the true Shroud but one of 2 other possibilities. one is a wrap used to cover a persons head before they are enshrouded. the other is the cloth used by the woman who wiped Jesus' face on his march w/ the Cross. this would explain why the Shroud did not work on Persephone, it was not the true Shroud. it might have the faith juice but not the true power of resurrection imbued within the one Harry just got. makes me wonder if he will try it on her to test it and get Marcone to owe him again.
the Plaque. : wonder if it some type of item that would allow someone to learn the true name of someone, even it's pronunciation. used in sealing someone or their powers, bind them/ entrap them.
the Knife/ Spearhead of Longinus : standard myth is it allows the user to become unbeatable. I think it is like Quantus was saying. something like and anti-entropy curse thingy. if anyone is a Marvel fan out you will recognize these two, Longshot and Domino, they had probability altering fields which had things go the right way for them in random situations. also the thing about it being able to kill anything even god-like beings fits it also.
Chalice : most myths involving this talk about healing/ rejuvenation/ immortality. wonder if this would be able to cleanse Black Magic taint or used to help Harry get rid of the WK Mantle?
just some WAGs but think a few might be close.