Hateful, odious, abhorrent, detestable, abominable are sometimes used with little distinction.
But hateful more frequently applies to something which excites actual hatred; odious, to something which is excessively disagreeable or which gives offense or arouses repugnance.
Something is abhorrent which outrages one’s sense of what is just, right, honorable, or decent.
Something is detestable which deserves scorn or contempt.
Something is abominable which is so abhorrent as to deserve execration.