I don't believe what Eve did closed them until the coming of Christ. That would mean that none of the people that lived in the time between Eve and Christ are in Heaven today.
They may have had to go about it in a different way, but many of those people are in Heaven today, as is obvious with Elijah.
That's a good point. It is generally believed that the holy men and women of the Old Testament existed is some kind of temporary state similar to "Limbo" while they awaited the Redemption. Heaven as it is understood would not have been open to them, but because of their role in the Covenant they would probably have had a good sense of what they were awaiting.