It is possible to reconcile the different reports of the men and angels without changing details and without resorting to redaction or mythologizing theories. Doing so leads to the conclusion the women encountered three men and three angels.
Mark reports a single young man; Luke reports two men. Reconciling these is straight-forward:
5 And entering the tomb, they saw a young man sitting on the right side, dressed in a white robe, and they were alarmed. 6 And he said to them, “Do not be alarmed. You seek Jesus of Nazareth, who was crucified. He has risen; he is not here. See the place where they laid him. 7 But go, tell his disciples and Peter that he is going before you to Galilee. There you will see him, just as he told you.” (Mark 16:5-7) [ESV throughout]
4 While they were perplexed about this, behold, two men stood by them in dazzling apparel. 5 And as they were frightened and bowed their faces to the ground, the men said to them, “Why do you seek the living among the dead? 6 He is not here, but has risen. Remember how he told you, while he was still in Galilee, 7 that the Son of Man must be delivered into the hands of sinful men and be crucified and on the third day rise.” 8 And they remembered his words.
8 And they went out and fled from the tomb, for trembling and astonishment had seized them, and they said nothing to anyone, for they were afraid. (Mark 16:5-8)
These women had two separate encounters with men inside the tomb. Mark reports the encounter with a single young man; Luke with two men. I have placed Mark before Luke however as Luke reports the women bowed their faces to the ground, placing Luke before Mark works equally well. In that case they saw the two men; bowed down; looked up and saw the one man.
This explains Mark's statement:
8 And they went out and fled from the tomb, for trembling and astonishment had seized them, and they said nothing to anyone, for they were afraid. (Mark 16:8)
Mark states the women did not speak to the men inside the tomb, a fact which is evident from both accounts and consistent with the reports them women did speak to the disciples outside the tomb.
Revelation and Matthew provide information as to the general identity of the three men:
11 Then they were each given a white robe and told to rest a little longer, until the number of their fellow servants and their brothers should be complete, who were to be killed as they themselves had been. (Revelation 6:11)
52 The tombs also were opened. And many bodies of the saints who had fallen asleep were raised, 53 and coming out of the tombs after his resurrection they went into the holy city and appeared to many. (Matthew 27:52-53)
After the Resurrection the bodies of the saints were raised and appeared to many people. As Revelation states throughout, saints are clothed in white. Therefore Mark and Luke each report one of the encounters with the resurrected saints Matthew reports.
This also helps to clarify the message Luke records the women heard inside the tomb: "Why do you seek the living among the dead (νεκρῶν)?" (Luke 24:5) νεκρῶν is plural. Since Jesus was buried in a tomb where no one had previously been laid, had the two men been speaking about Jesus they should use the singular. The actual plural use is consistent with seeing the two men as dead and now resurrected saints. In fact, they are referring to themselves.
Initial discovery of the tomb:
2 And behold, there was a great earthquake, for an angel of the Lord descended from heaven and came and rolled back the stone and sat on it. 3 His appearance was like lightning, and his clothing white as snow. 4 And for fear of him the guards trembled and became like dead men. 5 But the angel said to the women, “Do not be afraid, for I know that you seek Jesus who was crucified. 6 He is not here, for he has risen, as he said. Come, see the place where he lay. 7 Then go quickly and tell his disciples that he has risen from the dead, and behold, he is going before you to Galilee; there you will see him. See, I have told you.” 8 So they departed quickly from the tomb with fear and great joy, and ran to tell his disciples. (Matthew 28:2-8)
The two Mary's have an encounter with the angel of the Lord who rolled back the stone and gives instructions to go and tell the disciples. The women leave and tell the disciples.
John reports the final encounter:
11 But Mary stood weeping outside the tomb, and as she wept she stooped to look into the tomb. 12 And she saw two angels in white, sitting where the body of Jesus had lain, one at the head and one at the feet. (John 20:11-12)
There are two ways this can be reconciled.
"Mary" is Mary Magdalene: This method stems from seeing John's record as given in chronological sequence. Mary is never reported as entering the tomb; she remains outside until looking in and sees the angels. There is no difficulty reconciling the two angelic accounts. Since they are angels we presume they are not bound by natural obstacles and are capable of appearing in the tomb. In this case Mary looks into the tomb and sees two angels who came after Peter and the other disciple left.
"Mary" is not Mary Magdalene: There are several Mary's among the disciples: Mary the mother of Jesus, Mary the sister of Martha, Mary Magdalene, Mary the mother of James, and Mary the mother of Mark. As all four accounts appear to be careful when identifying Mary Magdalene, the second approach appeals to this fact and sees "Mary" as the other Mary in Matthew, not Mary Magdalene.
This harmonizes John and Matthew. Matthew reports two different Mary's coming to the tomb and leaving and, in this case, so would John. However, John has recorded the events of the two Mary's as two self-contained units. First is Mary Magdalene who goes to Peter and the other disciple who run to the tomb. Mary Magdalene does not go with them, rather she continues on (to another location) to tell the other disciples. At the same time the second Mary does not leave immediately; either she lingers or quickly stops and returns to the tomb. Then she looks in and sees the two angels. Thus John's account, like Matthew's, can be considered as detailing two different Mary's:
John 20:1-10 (she tells Peter and the other disciple)
John 20:18 (she tells other disciples)
The other Mary:
John 20:11-17 (sees the angels and Jesus who instructs her to go tell his brothers.)
In addition to more closely following the use of Magdalene, this method recognizes the disciples were not all staying in one location. 1 Since Mary Magdalene went first to Peter, the length of her trip will be determined by where Peter was staying; if he was in Bethany, she would have made the trip to Bethany to tell Peter then back to Jerusalem to tell the others.
This second method would mean the actual encounter Mary Magdalene had with Jesus is not recorded in any Gospel account:
18 Mary Magdalene went and announced to the disciples, “I have seen the Lord”—and that he had said these things to her. (John 20:18)
This should not be problematic. Her encounter with the Risen Lord, like Peter's, is not recorded.
1. John uses the plural homes: "Then the disciples went back to their homes" (20:10). This seems purposeful to make the point Peter and the other disciple who had been staying in one place, leave the tomb and go to two different places.