Northern Pines has introduced an interesting question about "how do we know who is saved?"
With respect to our liability to eternal punishment, we have to remember that there are two judgments. The first judgment is of our soul alone, after it has departed from our body at our natural death. After this judgment, the soul goes to Hades or to Paradise. We can call Hades Hell, but for many that is confusing, because Hell in English also refers to Gehenna, which will only appear at the Last Day, when our bodies are resurrected. At that time, we will be judged as soul and body together, and we will either be rewarded in Heaven or condemned in Gehenna.
There is a possibility for souls who were first condemned to Hades to be delivered from it later, through the prayers of the Church. Indeed, that is part of why we pray for the dead. There will be no deliverance from Gehenna however.
All those who die outside the Church will go to Hades: "He that believeth and is baptized shall be saved; but he that believeth not shall be damned" (Mark 16:16). This passage is so unambiguous as to scarcely need comment. In confirmation of this interpretation I can offer this passage from the vision of Blessed Theodora:
"Those who believe in the Holy Trinity and take as frequently as possible the Holy Communion of the Holy Mysteries of Christ, our Saviour's body and Blood - such people can rise to heaven directly, with no hindrances, and the holy angels defend them, and the holy saints of God pray for their salvation, since they have lived righteously. No one, however, takes care of wicked and depraved heretics, who do nothing useful during their lives, and live in disbelief and heresy. The angels can say nothing in their defence... [Only those] enlightened by the faith and holy baptism can rise and be tested in the stations of torment [that is, the toll-houses]. The unbelievers do not come here. Their souls belong to hell even before they part from their bodies. When they die, the devils take their souls with no need to test them. Such souls are their proper prey, and they take them down to the abyss."
So we know that those who die outside the Church will not be saved immediately, although we can hope that some may be saved later. If it possible for those who die within the Church to be saved from Hades, we can extrapolate from this that in general the condemnation to Hades is not irredeemable. This is however entirely up to God's secret judgment. The Church cannot offer prayers for those who died outside Her bounds.
The usual objection to this teaching is that those who die in ignorance of the Truth should not be condemned as those who have consciously rejected the truth. The answer is that yes if they have not consciously resisted the Truth, their lot will surely be better at the Last Day than those who consciously resisted. It is possible and indeed likely that God will have mercy on those who did not consciously resist the Truth, and we should certainly hope so. However, even those who do not know the Truth through ignorance will still go to Hades immediately after death. The passages above concerning the condemnation of heretics and unbelievers says nothing about their ignorance or lack thereof.
How do we reconcile this with God's justice? The answer is that we must distinguish between voluntary ignorance and involuntary ignorance:
"That servant who knew his master's will, and prepared not himself, neither did according to his will, shall be beaten with many stripes. But he that knew not, and did things worthy of stripes, shall be beaten with few stripes. For unto whomsoever much is given, of him shall much be required; and he to whom men have committed much, of him they will ask the more" (Luke 12:47-48)
and the commentary by Blessed Theophylact:
"Here some will object, saying: 'He who knows the will of his Lord, but does not do it, is deservedly punished. But why is the ignorant punished?' Because when he might have known he did not wish to do so, but was the cause of his own ignorance through sloth."
So only involuntary ignorance is excusable, although voluntary ignorance may itself attract mercy at the end to the extent it was unconscious resistance to truth. How do we know in whose case ignorance is voluntary or involuntary? Of course, we do not when it comes to our individual brothers; only God knows that. In general, however, we can say with assurance that there is no excuse for not believing in One God the Creator:
"From the beginning God placed the knowledge of Himself in men, but the pagans awarded this knowledge to sticks and stones, doing wrong to the truth to the extent that they were able." (St John Chrysostom)
Once an individual has acknowledged the truth of One God, there is no barrier to him having the full truth revealed to him, if he is willing to accept it. That is precisely what happened to St Barbara, who was brought up in polytheism, but through contemplation of Creation came to a knowledge of the True God, and in answer to her prayers, God revealed the doctrines of the Trinity and the Incarnation and Redemption. There is no such thing as invincible ignorance, in other words, since the Providence of God can overcome any adversity, provided the individual cooperates in his free will.