"If they remarry outside of the Church anyway, may they still take the sacraments?"
In Churches under the EP the answer is a resounding NO. I have seen this many times. The Synod of the GOA as recently as the late 80s or early 90s dropped the requirement of a remarriage in the Church of converts from Roman Catholicism. I know there is a requirement of at least a blessing for converts from generic Protestantism. For an Orthodox person to marry outside the Church means an automatic denial of at least communion until the union is regularized within the Church. Churches under the EP will allow three marriages in a lifetime, no matter what the reason for the end of the previous marriage. In the case of civil divorces, an exxlesiastical divorce must be obtained from the local bishop, which is an act of economia within the discretion of the bishop. He may or may not grant it. It should be noted that these are divorces and not annulments and are pure economia.
A couple other things worth mentioning here. The Orthodox perspective in regards to marriage is this: one man, one woman, together, forever. This 'till death do us part' thing we hear so much about came from somewhere else. Remarriage after the death of a spouse would also be considered a concession to human weakness. Not to suggest there's a perfect equation to be drawn here (two totally different tragedies to be sure), but the point to be made is that marriage in the Orthodox Church is taken very seriously. The commitment is eternal.
Also, we can't just marry any ol' person we meet. They don't have to be Orthodox (would be nice but is not madatory), but if they deny that Jesus is the Christ, the Son of God, the Second Person of the Trinity... forget about it. On the flip side, when it comes to non-Orthodox people we CAN marry, Roman Catholics actually top the list of preferred cadidates.