Yes, Catholics are allowed by the Catholic Church to receive communion in an Orthodox church, but they aren't not usually allowed to receive communion in an Orthodox church by the Orthodox.
Catholics are allowed by the Catholic church to receive in certain circumstances only though... such as when a Catholic needs the sacraments and there is no Catholic priest around, or Catholic Church nearby.
"Whenever necessity requires or a genuine spiritual advantage commends it, and provided the danger of error or indifferent ism is avoided, Christ's faithful for whom it is physically or morally impossible to approach a catholic minister, may lawfully receive the sacraments of penance, the Eucharist and anointing of the sick from non-catholic ministers in whose Churches these sacraments are valid. (CIC 844 ? 3)"
Catholics consider Orthodox sacraments to be valid (but illicit I think), we also recognize the Real Presence in their Eucharist, so in emergencies, Catholics could receive communion from the Orthodox, if the Orthodox church allows it. They do have exceptions though that I have heard of, especially in certain countries where the Orthodox and Catholic communities are quite close.
Orthodox members are allowed to receive in a Catholic Church by the Catholic church if they ask for it and meet all the other requirements Catholics would follow for receiving communion. But they are usually not allowed by the Orthodox Church to receive communion in a Catholic church, for the Orthodox doing so is usually considered renouncing their Orthodox faith in a way, because receiving Catholic communion means expressing full unity with Catholics. Because there are disagreements between the two churches this wouldn't be allowed.
"Catholic ministers may licitly administer the sacraments of penance, Eucharist and anointing of the sick to members of the oriental churches which do not have full Communion with the Catholic Church, if they ask on their own for the sacraments and are properly disposed. This holds also for members of other churches, which in the judgment of the Apostolic See are in the same condition as the oriental churches as far as these sacraments are concerned" (CIC 844 ? 3).
Catholics consider Orthodox communion to be valid. However, the Orthodox don't really say whether other church's sacraments or valid or not. They just believe that their sacraments are real. But for example One Orthodox might say that Catholic communion is really Jesus but another might disagree... I'm not Orthodox though so you may want their prov, I'm just speaking from observation/ research. For both churches though, there are always exceptions.
Now personally, I'm hoping one day, we won't have to ask questions like these and we'll be united again, make up, and share the same communion. I quote from a website though: "The Lord's timing, however, is not ours." We'll just have to wait, hope, and see