I'll have to answer from scriptural knowledge here, because I've never seen a Deva. Devas, according to the scriptures, are beings in a higher realm of existence. I guess if you want to call them heavenly beings, that would be so, but it's probably quite different to our usual perception of heaven. According to Buddhist philosophy there are different levels of beings. The human realm is one, above this are many more different levels of existences, which are considered the Deva worlds, and which are usually considered to be more pleasurable, with longer life spans, less Dukkha, etc. According to what I have read in the scriptures, yes, Devas can visit this world, I have had some Thais tell me that they can see them and that there are some around here from time to time. Whether that's true, I don't know - that's something which has been told to me.
Do I know any interesting stories of visiting Devas during the Buddha's life? I remember one story about Sariputta. Sariputta came from a very big family, his mother was a Brahmin worshipper and he had a lot of brothers and sisters. His mother had prejudice towards the Buddha and this new religion that was being formed because of the Buddha. And even though Sariputta was an Arahant, fully enlightened, his mother never accepted this and wanted him to return to the Brahmin religion. So she thought he had gone astray, and his brothers and sisters had also gone astray, even though they were also fully enlightened. She never accepted that Sariputta followed the Buddha.
When Sariputta realized that he was going to die soon, he returned to his mother's house, and she thought, "Oh how wonderful, he's finally realized that he's gone astray and he's coming back to the Brahmin religion". And she was very happy. He came with his attendant monk and she gave him his old bedroom to stay in. That night he became very ill. His mother wanted to know whether she could help him but he said, "No, I have my attendant to help".
A Deva appeared in the house and because Sariputta's mother was a Brahmin she became overawed by this beautiful Deva who was shining through the house. She asked, "What do you want?" and the Deva replied "I have come to help and pay respect to Sariputta". "You have come to pay respect to my son?" "Yes". So the Deva went to where Sariputta was lying ill. Sariputta said, "No, thank you, I have my attendant, I don't need you", and so the Deva disappeared.
Now this happened a few times during the night, more and more beautiful Devas appeared, wanting to help and pay respect to Sariputta who was dying, and his mother was more and more overawed by this situation of these heavenly beings coming to pay respect to her son. Until finally Brahma (the highest deity of her religion) appeared in all his glory and she asked, "Why have you come?" "I've come to help and pay respect to Sariputta". "Brahma is coming to pay respect to my son?" And Brahma went in to see Sariputta and then Sariputta said, "No, it's ok, I have my attendant", so Brahma disappeared.
Then she started thinking, "Well, if Brahma has come to pay respect to Sariputta, what then is the Buddha?" And she started to contemplate, perhaps opening to the possibility that the Buddha may be greater than she had thought. And through contemplation on the Buddha apparently she became a stream enterer, that's the first level of Enlightenment. After that she became a follower of the Buddha.
It was through Sariputta's Compassion that he went to his mothers' place, trying to show her the path out of suffering before he died. So when perhaps our parents may not agree with us, we can have a little more patience realizing that it's not new. And to understand that even Sariputta, the right hand disciple of the Buddha, whose wisdom was apparently higher than anybody except the Buddhas', can be rejected by his parents.