As hard as it may be to swallow, YHWH can assume any form He desires. In Bereishis 18 we read
"The LORD (YHWH) appeared to Abraham near the great trees of Mamre while he was sitting at the entrance to his tent in the heat of the day. Abraham looked up and saw three men standing nearby. When he saw them, he hurried from the entrance of his tent to meet them and bowed down to the ground."
In true Middle-Eastern fashion, Abraham insisted that his guests have a servant wash their feet, stay for a little nosh, and depart only after they had been refreshed, perhaps in the cool of the evening.
Numerous times G_d's name (YHWH) was used in chapter 18 (vv.10, 13, 16, 17, 19, 20, 22, 26, and 33). Interestingly, the next chapter continues the narrative begun in chapter 18 and says in v.1,
"The two angels arrived at Sodom in the evening, and Lot was sitting at the gateway of the city. When he saw them, he got up to meet them and bowed down with his face to the ground. 'My lords,' he said, 'please turn aside to your servant's house. You can wash your feet and spend the night and then go on your way in the morning."
Lot importuned, and the two angels agreed to spend the night in Lot's house. Like his uncle Abraham, Lot made a meal for his guests. Before they went to bed, however, perverts from Sodom came to Lot's house with sex on their minds. I add this information because it is clear from chapters 18 and 19 that the men who first visited Abraham and--minus one--then visited Lot, appeared as male human beings. They were evidently capable of conversing, having their feet washed, eating, drinking, sleeping, walking--all obviously human abilities and activities.
How do we know that one of the three men in chapter 18 was YHWH in human form? Because Abraham addressed Him as YHWH. In the conversation Abraham had with YHWH, he not only addressed G_d as YHWH, but he said something interesting,
"Will not the Judge of all the earth do right?"
Who besides YHWH is capable or has the authority to judge the whole earth? The answer, to me anyway, is YHWH and only YHWH.
Moving on, then, to Shemos 24:10, we read that the 70 elders, along with Aaron, Nadab, Abihu, Hur, and Joshua physically saw the God (Elohim) of Israel. Moreover, God did not "raise His hand against" these leaders of the Israelites but allowed them to see Him and to eat and drink in His physical presence.
I say "physical presence" because, again, G_d is free to assume any form He so chooses. If through the angel of YHWH G_d could cause a donkey to speak (see Bamidbar 22), it's not too big a stretch to believe He could assume human form. This is what I believe the 70 elders beheld.
Notice when Moses parted from the elders, it was at the invitation of YHWH (v.12), and Moses and Joshua ascended the mountain of G_d. Instead of human form this time, YHWH appeared as a cloud that covered the mountain, and
"For six days the cloud covered the mountain, and on the seventh day YHWH called to Moses from within the cloud" (v.15).
From a distance, the Israelites perceived the glory of YHWH as "a consuming fire on top of the mountain" (v.17). It is not coincidental that during their wilderness wanderings, the Israelites were led by both a pillar of cloud and a pillar of
fire. Centuries later, rabbis used the extra-biblical term shekinah, a form of the Hebrew word that means literally "he caused to dwell," signifying that the pillar of cloud and the pillar of fire comprised a divine visitation of YHWH (see Shemos 13:21,22; 14:19,24; 33:9,10; Bamidbar 12:5; 14:14; Devarim 31:15).
I will not take the time or space to address the separate (though perhaps relevant) topic of "the angel of YHWH," which appears numerous times in Tannakh. Perhaps someone well-versed in the Talmud and the Midrash would like to share what they have to say about this heavenly visitation.
In conclusion, what the 70 elders, et al., saw was evidently G_d in human form and appearance. What neither they nor Moses (and Abraham) saw was the "face of G_d" as reflected in all His goodness:
"And YHWH said [to Moshe], 'I will cause all my goodness to pass in front of you, and I will proclaim my name, YHWH, in your presence. I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. But,' He said, 'you cannot see my face, for no one may see me and live'" (Shemos 33:19).
"'Then I will remove my hand,' [G_d said] 'and you will see my back; but my face must not be seen'" (v.23).
Moses beheld, as it were, the after-affects of G_d's passing before him as Moses stayed "in a cleft in the rock," covered by the hand of God (v.22).
From the Notes of the NET online Bible (net.bible.org/#!bible/Exodus+33:11) comes the following: Gesenius notes that sometimes a negative statement takes the place of a conditional clause; here it is equal to “if a man sees me he does not live” (cf. Gen 32:30; Deut 4:33, 5:24, 26; Judg 6:22, 13:22, and Isa 6:5). The Niphal imperfect could simply be rendered “will not be seen,” but given the emphasis of the preceding verses, it is more binding than that, and so a negated obligatory imperfect fits better: “it must not be seen.”
In conclusion, God has, as it were, two faces: one that a number of human beings have actually seen in human form or in a vision (e.g., Isaiah in his prophecy, chapter 6:1-5), and a second that no human being can ever see and live. G_d's holiness, goodness, and glory can be seen and appreciated by a privileged few, but only as mediated through a cloud, a fire, a whirlwind, a burning bush, a vision, and a human being (am I leaving anything out?); His transcendent essence, however, cannot be seen. Such is the immanence and transcendence of G_d!