It is indeed ironic that Heathcliff should be regarded as the epitome of barbarism—of all that is wild, impulsive, and savage—when it is the supposedly respectable Hindley Earnshaw who behaves abominably, not just towards Heathcliff but towards everyone else as well. On the surface, Hindley appears to be the ideal representative of so-called civilized society; he has education, wealth, and prospects. However, the abusive way he treats others (especially Heathcliff) is anything but civilized and reveals a heart of darkness beneath his respectable exterior.
With regards to symbolism, ghosts are used by Brontë to represent the persistence of memory in people's lives. The bleak moors which form the backdrop of most of the book's action are haunted, both literally and figuratively. Whether the sightings of ghosts are meant to be real or merely a figment of overactive, superstitious imaginations—there's no doubt that, within the narrative, ghosts symbolize the way in which the very landscape has become deeply infused by the abiding memory of Heathcliff and Catherine: two restless spirits.
With regard to Emily Bronte's novel, Wuthering Heights, I don't know that I can help you much, but the most obvious irony is that Heathcliff does all he can to get Wuthering Heights, mostly because he cannot have Catherine (and because of how Hindley treats him).
Once he wins the house from Hindley while gambling, the reader would expect Heathcliff to be happy, finally. He bested Hindley, and he is the master in the home where he was treated like a servant after his adoptive father died. However, the hole within Heathcliff is just as deep, and the more he hurts those around him, from his own suffering, the more he suffers himself, never finding happiness.
Before Heathcliff leaves Wuthering Heights after Hindley's poor treatment, he overhears Catherine speaking of why she could not marry Heathcliff. He leaves the Heights before he hears anymore. The irony here is that had he listened further, or talked with Catherine before leaving, he would have known that she loved him, but that she did not believe they would make a good match. This might have given him hope, knowing someone he cared for loved him, to make the most of what he was able to do for himself while he was away (returning educated, with money), to enjoy a much fuller life. His obsession devours his soul and robs him of that opportunity.
Later, Catherine collapses in his arms, and dies never regaining consciousness. His only solace is begging her ghost to haunt him. We know this happens soon before he dies. In death they are reunited as their caskets lie next to each other, with the sides open so that as they return to dust, their remains can mingle over the years. Perhaps this is ironic that they are finally able to be together, but only in death.
In terms of symbols, I can offer only one, which also presents an irony: the moors. When the novel opens, Lockwood, to whom Nellie tells the story of Wuthering Heights, does not like walking on the moors at night because he is frightened; ironically, Heathcliff and Catherine love spending long hours on the moors growing up. The landscape does not intimidate them. This may symbolize a wild, impetuous nature, something they both share.