Is it licit for a Catholic (east or west) to receive the Eucharist in an Orthodox Church, and vice-versa? Can a Catholic fufill their Sunday obligation at an Orthodox Church?
The situation concerning intercommunion between Orthodox and Catholics is tricky. Following Vatican II, Pope Paul VI lifted all excommunications against the Eastern Orthodox. Likewise, Patriarch Athenagoras of Constantinople lifted all excommunications against Catholics. So, judging by this action, it would seem that we should be back in communion. But we aren’t. If we aren’t excommunicated from one another, but aren’t in communion, then what the heck is the status of our relationship?
As the matter now stands, Eastern Orthodox bishops do not allow Catholics to receive the Eucharist. We should respect their discipline, and refrain from doing so. When there is no Catholic Church nearby, you can fulfill your Sunday obligation by attending an Eastern Orthodox Church without receiving the Eucharist.
In contrast, Eastern Orthodox Christians are welcome to receive the Eucharist in any Catholic parish, but only if their bishop allows them to do so.