Those three men were materialised angels and it is through them that God appeared to Abraham, this is not a literal appearence.
Some commentators will agree with you Grenndawn...others feel it was the same manifestation as Christ performed( yet they never explain that jesus came through actual birth, and the others simply "appeared".)
Another notible one says it was the Lord (Yahweh I assume) himself manifested in the flesh.
Here are some samples,
John Wesley commentary
18:1 This appearance of God to Abraham seems to have had in it more of freedom and familiarity, and less of grandeur and majesty, than those we have hitherto read of, and therefore more resembles that great visit which in the fulness of time the Son of God was to make to the world. He sat in the tent - door in the heat of the day - Not so much to repose himself, as to seek an opportunity of doing good, by giving entertainment to strangers.
18:2 And lo three men - These three men were three spiritual heavenly beings, now assuming human shapes, that they might be visible to Abraham, and conversable with him. Some think they were all three created angels; others, that one of them was the Son of God. He bowed himself towards the ground - Religion doth not destroy but improve good manners, and teaches us to honour all men
18:2 And he lift up his eyes and looked, and, lo, three a men stood by him: and when he saw [them], he ran to meet them from the tent door, and bowed himself toward the ground,
(a) That is, three angels in the shape of men.
18:3 And said, My b Lord, if now I have found favour in thy sight, pass not away, I pray thee, from thy servant:
(b) Speaking to the one who appeared to be most majestic, for he thought they were men.
18:4 Let a little water, I pray you, be fetched, and c wash your feet, and rest yourselves under the tree:
(c) For men used to go bare footed in those parts because of the heat.
Commentary Critical and Explanatory
on the Whole Bible
Genesis 18:1-8. ENTERTAINMENT OF ANGELS.
1. the Lord appeared--another manifestation of the divine presence, more familiar than any yet narrated; and more like that in the fulness of time, when the Word was made flesh. plains of Mamre--rather, terebinth or oak of Mamre; a tall-spreading tree or grove of trees.
sat in the tent door--The tent itself being too close and sultry at noon, the shaded open front is usually resorted to for the air that may be stirring.
2. lift up his eyes . . . and, lo, three men--Travellers in that quarter start at sunrise and continue till midday when they look out for some resting-place.
he ran to meet them--When the visitor is an ordinary person, the host merely rises; but if of superior rank, the custom is to advance a little towards the stranger, and after a very low bow, turn and lead him to the tent, putting an arm round his waist, or tapping him on the shoulder as they go, to assure him of welcome.
3. My Lord, if now I have found favor--The hospitalities offered are just of the kind that are necessary and most grateful, the refreshment of water, for feet exposed to dust and heat by the sandals, being still the first observed among the pastoral people of Hebron