When I recognize that an author is using symbolism I am always intrigued to understand what their other message is, and sometimes the translated symbolic message is so advanced, and so not what the author appears to be about, that I wonder if they have included their symbolism unconsciously, and the message is directly from their God.
J K Rowling, however, is using symbolic language quite consciously, and in a common sense sort of way. Here is a bit of it:
Air - this is Ravenclaw house. It's animal is the golden Eagle. it's emblem is the tiara of Roweena Ravenclaw. It's colors are blue and bronze
Location: Ravenclaw Tower, which is located on the west side of the castle
The common room, like the other House common rooms, is decorated in House colours (blue and bronze silk wall hangings, in this case, and a midnight-blue carpet decorated with stars). The room is wide, circular, and very airy, with a domed ceiling painted with stars, and walls with graceful arched windows that provide a spectacular view of the surrounding mountains. There are bookcases, tables, and chairs, and opposite the entrance is another door leading to the dormitories. Beside this door is a plinth on which stands a life-size statue in white marble of Rowena Ravenclaw wearing her diadem
Fire - this is Gryffindor. It's animal is the Lion. It's emblem is the sword. it's colors are red and gold. The entrance is located behind a large painting of a Fat Lady in a pink silk dress. If you know the right password to tell her, she swings open to reveal a round opening in the wall. The common room contains a lot of squashy armchairs, a fireplace, and tables. The fireplace is connected to the Floo Network.
Earth - this is Hufflepuff. It's animal is the black Badger, a burrowing animal. It's emblem is the cup of Helga Hufflepuff. It's colors are yellow and black. Of their quarters we hear - "as dissimilar as possible" from the Potions classroom. As we have seen in the other common rooms, it is decorated in House colours, which in this case means that there are lots of yellow hangings; like Gryffindor Tower, it has a lot of comfortable armchairs. There are "little underground tunnels leading to the dormitories, all of which have perfectly round doors, like barrel tops" (BLC, JKR).
Water - This is Slytherin House. It's animal is the snake. It's emblem is the locket of Salazar Slytherin, whose secretive and enclosing properties are comparable to the chamber of secrets. It's colors are silver and green. The Slytherin common room is a low-ceilinged, dungeon-like room with greenish lamps and chairs, with skulls all around and views into the lake.
This symbolism would identify the houses with the body so: head - Ravenclaw, heart - Gryffindor, stomach - Hufflepuff, and lower abdomen - Slytherin. It also identifies certain houses with directions. Ravenclaw is on the west side of the castle, thus intellect is associated with west, and loftiness in general. And we can deduce that if the mountains are to the west, around the castle than the lake must be to the east, and thus Slytherin is associated with east and emotion, especially painful emotion as is further demonstrated by the painful childhood of Snape, and the suicide of it's ghost, the Bloody Baron. This leaves north and south for the other two houses. North is traditionally associated with spirituality and south with physicality, so very likely north belongs to Gryffindor and south to Hufflepuff, though I am only guessing.
She has kept with traditional symbolism for directions in so far as I can tell, but has broken with tradition and used common sense symbolism for their emblems. Tradition associates the sword with air/intellect, the cup with water/emotion, the wand with fire/soul or spirit, and the platter or coin with earth/physicality. Perhaps because everyone had wands she needed to change things, or perhaps she wanted symbols that added something to our understanding of the properties of the four elements. She gave Air a Tiara, quite an appropriate symbol of mental brilliance. Fire was given the sword. The sword is truth, always - as far as I have seen. Is this to say that it is spirit that is the source of bravery, and that spirit is the source of truth. I think so. Earth is given the cup, and it is symbolic of kindness and generousity, which Helga Hufflepuff displayed well. It sort of speaks to plenty, and the generosity of nature, which feeds and suports us and gives us this lovely play ground to evolve in. And water got a locket, a sort of secret chamber in which evil was hidden. That goes well with her story, but is she giving water a bad rap? Not if you think of water as a force for chaos and erosion, which it is. Also, she has identified water with negative emotions; the green and murky kind which we hide from others so that they perhaps fester in secrecy. Jealousy. Envy. Insecurity. Draco Malfoy displays all of these.
The four house ghosts give us more confirmation of, and information about J K Rowling's ideas on the four elements. I have already mentioned the pain which drove the Bloody Baron to murder and suicide. But the Fat Friar is also apt for Hufflepuff, as is the cold maiden, Helena Ravenclaw. Nearly Headless Nick is a bit of a puzzle. Does she mean to say that people driven by spirit, the truly heroic, often don't pause to think. They aren't so much clever as virtuous? This is certainly true of Harry, throughout the book. He does the right thing, usually without regard for his own well being. And it is true of Neville, when he defies his friends in the first book and Lord Voldemort in the last.
The four friends - Lupin, Sirius, James, and Peter also give us more to ponder. Lupin, associated with the moon, and painful emotions seems to be the watery one. James, the seeker, would be fire. Sirius, as different from his family as he could be, and named after the brightest star would be air. And Peter the rat would be earth. Each gives us another view of these elemental personalities. Lupin is filled with painful emotion but he takes it to a different place than the typical slytherin. Instead of tearing others down to feel better about himself, he has humility. James shows us the negative side of fire, arrogance and thoughtlessness. Sirius is an air personality with passion, he deeply loves James, and is a man of action. Recall also that Sirius, the star was called the dog star, and the scorcher, as it seemed to herald in the hottest days of summer, the dog days. Peter seems to be the dark side of earth, a survivalist; one who will betray anything for the sake of his own physical survival.
There is another tradition which associates the four elements with the four upper chakras. These correspond to the endocrine glands in the human body. In this tradition water is associated with the Thymus, near the heart. Air to the Thyroid, in the throat. Fire to the Pineal gland which regulates wakefulness and sleep, and is located near the back of the brain. And Earth, as diamond, the crown chakra and master gland. This symbolism is seen in our common playing card deck - water is hearts, earth is diamonds, fire is clubs(a descendant of the tarot suit of wands), and air is spades(a descendant of the tarot suit of swords). In this tradition the four fixed signs of the zodiac - Taurus/earth, Leo/fire, Scorpio/water and Aquarius/air - also correspond to the four upper chakras. These are the four living animals mentioned in the bible, and are to be seen on old European cathedrals, with the eagle replacing the scorpion, a well known alternative symbol. Their importance is that the three lower chakras control everything that makes one human, in a muggle sense of the word; while the four upper seals represent evolution spiritually. The heart chakra is love. The throat chakra is expression of love. the pineal is seeing Divinity in all people and things. And, the pituitary is seeing the Divinity of self.
The four treasures of the Tuatha De' Danann fall into this tradition, with the Undry Cauldron corresponding to water and the heart chakra due to it's power of feeding and healing; the Sword of Nuada being a sword of truth equates with air and the throat chakra, speaking truth being a sure spiritual weapon against ignorance; The Lugh's spear Luin symbolises fire and the quickening when the pineal is activated; and the Lia Fail, stone of kingship, represents earth, exalted. The king was also the spiritual leader of his people. He was earth exalted, and thus the stone recognized him.
It is possible certain characters in the Harry Potter books are meant to exemplify these upper four, but it is not explicitly shown. However the three lower chakras/seals are seen in the deathly hallows. The three lower ones are sexuality; especially male, as the female sexual glands are higher, and more associated with the second seal/chakra, which is emotional pain. And the third is power, the will to have our own way, to control. As deathly hallows we see the first seal in the wand, which is a power tool, but more brutish, and phallic. The second seal/chakra, emotional pain (people who dwell primarily in this seal are very psychic, and likely to see thinks of the next world) is symbolized by the black stone. The cloak of invisibility is left to correspond to the third seal/chakra, and at first it seems an ill fit, but if true power comes from knowledge, what better way to gain knowledge than to be able to go anywhere undetected. That Harry becomes master of the three is to say that he has evolved beyond the human condition, and of course the voluntary self sacrifice, for love of his friends and peers, and subsequent resurrection, makes him a Christ-like figure of the sacrificial lamb sort.