Odiousness has degrees. There are things that are more and less odious. And, odiousness is a matter of perspective. One person's execration is another person's delight. The Bible says that the meaning of the cross is an "offense." (Galatians 5:11). To some people it is odious and to the believer it is delightful.
The above is somewhat true, scripture does speak of the fragrance of Christ and a smell of death:
To God we are the fragrance of Christ, both among those who are being saved and among those who are on the way to destruction; for these last, the smell of death leading to death, but for the first, the smell of life leading to life. Who is equal to such a task? (2 Corinthians 2:15-16)
Why do you bring up this notion of odiousness to the unbelieving? The
Penal Substitutionary Atonement (PSA) theory is not the gospel; PSA is a doctrine that some teach and that many reject.
Imagine the most loathsome account of the meaning of the cross. The most detestable, vile, repugnant, and defiling explanation to the carnal man. That meaning is the true, Biblical, and holy meaning of Christ's work on earth.
I hope you are not seriously contending that the most disgusting imaginations of unbelief are true. That simply because some loathsome idea about the gospel is conceived by those who reject the gospel that this loathsome idea must therefore be the truth. That would be absurd.
We must continue to teach Jesus's wrath-bearing substitution even though it is “foolishness to those who are perishing”, because we know that it is the power of God to those who believe and embrace it, resulting in salvation (1 Cor. 1:21). Praise be to Jesus Christ and his marvellous, merciful and delightfully offensive atonement!
You might want to believe that God's wrath was poured out on Jesus Christ while he was suffering on the cross and when he died. But that belief implies that God the Father poured his wrath out on God the Son and that means that God was wrathful towards God. I wonder if you believe that God poured out his wrath on God? And that God hid his countenance from God? And since Christ became a curse for us do you believe that God cursed God?
I am not saying that you are an unbeliever, but we all must struggle against our carnal nature that would recoil with horror from the Gospel. The true Gospel that Jesus came to herald was one that was so offensive that He pronounced a special blessing on all those who were able to receive it: “And blessed is he, whosoever shall not be offended in me” (Luke 7:23). It takes a special blessing not to be offended in Christ.
It is interesting that, after your words in the previous two paragraphs, it has occurred to you that what you wrote could be construed as calling me (and by implication all who do not teach and believe PSA) non-christian.
You are, as your words so clearly say, calling all who do not share your views on PSA 'carnal', aren't you?
People -- including Christians -- if they hear and understand the true Gospel, and see and hear the true Jesus, will in some measure be offended or will be unable to believe and be saved. Together, we should encourage each other to embrace what would be offensive to the natural man.
The above paragraph is a little muddled, you say that Christians "will be unable to believe and be saved", which appears to be an oxymoron.