Let me take these passages one at a time. In Genesis 18:9-10, one of the three angels asked Abraham where his wife was. Verse 10 has, "Then the Lord said." The problem her is that the Hebrew has literally "Then he said." For this reason, it is hard to know who "he" is. It seems likely that "he" is one of the angels. Farther down, in verse 13 has "Then the Lord said to Abraham." Is this a reference to something one of the three angels said, or is God actually speaking? The answer is that we do not know. For the Jews, angels were messengers of the Lord (Hebrews 2:2). In fact, angel means messenger. For this reason, when a messenger speaks, it is entirely possible that the Bible writer will say that "the Lord" spoke. In some situations Bible writers say that God spoke to Moses on Sinai, but in others it says that God spoke through angels. This seems to be implied by Hebrews 2:2. Obviously, there is a big difference between God literally speaking to someone–producing sound without using the voice of a person or an angel–and God speaking through a person or an angelic being. However, the biblical language will not always nail down the answer for us. Of course, one can say that it does not really matter if God is speaking directly or if he is pronouncing something through an angel. It is customary for us to say "The President said" or "The King said" when in fact it was a spokesperson, not the king or Prime Minister who actually spoke.
As for Exodus 14, there is a reference to the Lord speaking to Moses (v 15), followed by a statement that "the angel of the Lord, who had been traveling in front of Israel’s army withdrew…" In this case, I believe the one who spoke to Moses is not the angel who moved behind Israel, but the nature of the angel is enigmatic. As for Numbers 9:15, I do not see an angel here. When the column of fire moved, that was how God told the people to move. When it says, "At the Lord’s command," I assume the command was given by the moving of the cloud/column of fire. With Judges 13, it seems that this was an angel. Samson’s parents are not speaking by inspiration when they said "We have seen God." They saw an angel and told their friends that they had seen God. I do not think you can learn anything doctrinally or otherwise from this exclamation of Samson’s parents.
John Oakes, PhD