The earth shook - See Exodus 19:16-18.
The heavens also dropped at the presence of God - That is, dropped down rain and food. The idea is that the very heavens seemed to be shaken or convulsed, so that rain and food were shaken down - as ripe fruit falls from a tree that is shaken. Compare the notes at Isaiah 34:4. So also, Isaiah 64:1-3. The meaning is not that the heavens themselves dropped down, but that they dropped or distilled rain and food.
Even Sinai itself was moved - This was true; but this does not seem to be the idea intended here, for the words “even” and “was moved” are not in the original. The Hebrew is, literally, “This Sinai;” meaning probably” this was at Sinai,” or, “this took place at Sinai.” The correct translation perhaps would be, “The heavens distilled rain at the presence of God, this at Sinai, at the presence of God.”
At the presence of God, the God of Israel - The whole region seemed to be moved and awed at the presence of God, or when he came down to visit his people. The earth and the heavens, all seemed to be in commotion.