The origin of the word stems from the superstition of Roman people. They were careful to examine any number of chance circumstance and happenings for omens prior to a large battle or other massive undertaking. The omens came in many forms and were interpreted either to foretell something good or bad. Few men who desired a task would ignore a good omen but a bad omen may from time to time be ignored. Sometimes to his doom. The forsaking of the "wisdom of the omen" was considered ab ominous against the omen. Over time the initial meaning which inspired fear and loathing connected with going against the omen was easily transferred to disgusting things in general. Thus Abominable.
Not much has changed, people are still seeking omens in the world around them. Chance events are still consulted as if they were authoritative. Every day millions read the horoscopes or simply look to the weather to determine their fate (I'm not talking about trying to see if you should wear a rain jacket). Such is not the work of a Christian. The LORD has made it clear in texts like Deuteronomy 18:10; Leviticus 20:6 and Ezekiel 13:6-8 that seeking supernatural knowledge apart from God is an evil work and sinful.
Consulting the tarot cards, life lines and madam Edna's crystal ball are Satan's domain. Woe to the ones who entangle themselves in them. God is the source of knowledge. He alone holds the future. Seek your answers from the only true God. He alone can answer with authority.
People also look for omens from God in order to prove that he exists. I remember watching a movie some time back where a man was screaming at the ceiling, "Come on God if you're really there you can knock over this glass of water!" Finally the guy gives up and bumps the table spilling the water – whereupon the guy looks up toward heaven in awe. (I may have misremembered the scene if you can help out here please do.)
Jesus turned his scathing remarks upon the Pharisees and Sadducees who came to him seeking for a sign (omen).
"An evil and adulterous generation seeks after a sign; and a sign will not be given it, except the sign of Jonah." – Matthew 16:4
Ultimately Jesus did offer even them a sign but it wasn't a magic trick in front of their eyes. It was his crucifixion, burial and resurrection played out in plain view in front of the world. So not all signs or omens are bad. John makes it clear that the signs (omens) he recorded were written with the express purpose of demonstrating that Jesus is the Christ the very Son of God and thus believing them people might be saved. (John 20:30-31).
In this case it is most definitely an abominable thing to go against the omen.