You have given your sash to your flock, O Virgin most glorious, as a bond that is most secure, which carefully keeps us from all kinds of danger and which by divine power preserves us from defeat by adversaries — from the Aposticha for August 31
Within the tradition of the Church, there are plenty of things that can be translated into a fantasy RPG world as "magic" items. These can be broken down into three broad categories: sanctified items, holy objects and relics.
Several times during the year, various foodstuff is brought to the church to be blessed and sanctified. These include, but are not limited to: oil, grapes, bread, water, and cakes. In game terms, these items, when consumed, might heal a hit point or bestow a bless spell for a certain amount of time, etc. Most of these items would have limited availability, because the services that sanctify them occur only once or twice a year. Thus, a fantasy world could include a calendar with several feasts (the Orthodox Church has twelve major feasts besides Pascha, aka Easter). Foodstuff is usually blessed on or around several of these feasts. This could add an interesting dimension to any RPG world.
Throughout the Orthodox world there are miracle working icons. For example, at the Iveron Monastery on Mt. Athos there is a icon of the Theotokos (the Virgin Mary) that was stabbed with a sword by a pirate. The sword hit the Theotokos in the chin and the icon began to bleed. The encrusted blood is still there today. Other icons are known to "weep" — myrrh flows from the eyes of the saint depicted. In addition, there are several objects, such as the sash worn by the Theotokos from the hymn above, that were worn or used by various saints.
In game terms, these could act as spell storing devices that can hold and then cast a number of divine spells a day. The myrrh from a weeping icon, when placed on a wound, might bestow a healing spell of some kind. The use of this myrrh could be limited to once per day or week per person. Other items, such as shoes or belts could act as variations on regular magic items — like boots of leaping or a ring of protection. This way, however, the item has a name and a backstory.
In churches around the world, bones and body parts of saints are kept within churches and places of pilgrimage. As macabre as this sounds, it has to do with Christian anthropology, which has a holistic understanding of the human person. The body is an integral part of who we are. A saint has been transfigured by God and therefore their body — their remains — have been imbued with holiness. One of the most dramatic examples of this can be seen in Thessoloniki with the body of St. Demetrios. His body continuously exudes myrrh. So, when you go to his reliquary, you are assaulted by this sweet perfume that smells better than anything in the world.
In game terms, these would be more along the lines of artifacts that would be able to do miraculous things; however, there should be a danger associated with using them — if used in a selfish or evil way, curses, bad luck, or extra attention from evil organizations or creatures should quickly follow. On top of that, there should be no end to beings that would want to try and steal or destroy such objects given the opportunity.
This is a difficult subject to tackle in a fantasy RPG, given the metaphysical, spiritual and practical ramifications of including it in a game. However, I wouldn't discourage a player who wanted to play a character for whom taking communion on a regular basis was part of their story. Personally, I like to reward that kind of effort in my players and this reward often takes the form of home-brew mechanics, XP rewards or special abilities.
In terms of communion, I would want to do something that encouraged players to make it a part of their characters' lives without it breaking the game. Personally, I allow characters who have gone to the trouble to taking communion to have one re-roll during a session. This gives players another expendable resource that can increase the tension of a session, be fun, and not overpower the game.