Abhorrent describes something truly horrible like finding a dead rat in your soup, but something aberrant is just abnormal, like a cat in a pink fedora.
Abhorrent means disgusting or detestable. When you abhor something, you loathe it. Its Latin root means, "to shudder, recoil," which is what you do when faced with something abhorrent like a zombie, or or in these examples:
She said sanitary conditions in the emergency room were abhorrent. (Seattle Times)
If I thought monarchy abhorrent, for example, I would not seek British citizenship. (Washington Times)