The primary way of communication for man is speech. Speech produces symbolic sounds that requires the other persons hearing it to know what the sounds mean. As sounds, human speech cannot completely translate the spiritual content of the mind.
Angels do not have bodies, they cannot communicate verbally. They are able to open their minds and reveal the whole though, as it were, without the channel of symbolism, sound and words, which is a higher and better word form of expression. (ewtn.com, Pascal P. Parente, The Angelic Nature and its Operation, Ch. 2) Angels use a universal language which is unknown to us. On the other hand, they are also able to produce human speech and evident in many apparitions.
Angels are always in communion with God and obtain their ineffable knowledge by contemplating his glory. They are endowed at creation with certain universal truths suited for the work God assigns them, however this knowledge is never complete in God's ongoing plan for the universe, so they continually learn either directly from God or through the illumination (giving of truth) from the higher hierarchies of angels.
Angels means messenger and in the history of God to man. They have at times appeared and spoken with men in various ways.
By Juande Valde's Leal
Here we see Abraham ready to sacrifice Isaac when an Angel of the Lord called out from heaven, Do not lay your hand on the boy, ...Do not do the least thing to him. For now I know that you fear God, since you did not withhold from me your son, your only one.(Gn22:12) In this case, Abraham did not see the angel but only heard his voice.
Here the angel Raphael tells Tobiah to remove the gall from the fish with which to heal the blindness of his father Tobit. Here Raphael took on a human form to guide Tobiah from Israel to Media and back. Tobiah thought that his guide was just a young man who knew the way, only toward the end of the journey did Raphael reveal his identity, "'I am Raphael, one of the seven angels who stand and serve before the Glory of the Lord.' Greatly shaken, the two of them fell prostrate in fear." (Tob 12:15)
Here we see Jesus healing a man who could not in time enter the pool of Siloam in time when the water stirred. Many recent translation of the Bible leave out this verse because it is not found in older manuscript of the Bible. "At certain times an angel of the Lord would go down into the pool and stir up the water.", (Jn 5:4) Here the Angel of the Lord made his presence known not by appearing but by acting (stirring of the water). If an angel of the Lord did not stir the water, "Who or what stirred the water to cause a miracle?" Since a person was healed each time, it was not a natural event but a divine one. God usually performs miracles through intelligent creatures. Here there is no human being to stir the water, so what is left, an invisible creature. If it was not an angel stirring the water, it was God himself which is not likely. In this case God chose to heal the sick through the humanity of his Son.
Joseph was troubled when he discovered that Mary was with child. It was his intention to divorce Mary quietly but an angel intervened. "The angel of the Lord appeared to him in a dream and said, Joseph, son of David, do not be afraid to take Mary your wife into your home. For it is through the holy Spirit that this child has been conceived in her." (Mt 1:20)
So, there are many ways an angel can speak to human beings.