First of all, let me guess where your confusion comes from. Probably you have not looked up「よっぽど」yet.
Do you know that「余(っ)程」is read as 「よほど or よっぽど」and have same meaning, so I think naruto mentioned entry No.1 of「よっぽど」in the dictionary I linked.
Anyway,I will give my best shot to your summary:
- I am not sure about its etymology though, 「よほど/よっぽど」means "to a great degree" mainly. You might think「よほど/よっぽど疲れてたんだな」if your friends started to sleep on the couch just after coming back to the house. This one intensifies how tired they are.
- It depends on the context, in a different setting, I think it's more of a set phrase
・「普段{ふだん}は冷静{れいせい}な彼{かれ}が血相{けっそう}を変えて出ていった。余程{よほど/よっぽど}のことがあったに違いない。」:
"He, who usually was a calm guy, left with his face burning red. There must have been something serious had happened to him."
In this sentence, you can guess something wrong might have happened to him seeing his face. It's saying more of something urgent than something unexpected.
- I think it is kind of a common phrase.「よほどのことがない限り。」would describe both "unless a very important thing happens" and "it is really unlikely to happen".
Interestingly, the headline of this article explicitly states the possibility by quantity : 「新型{しんがた}コロナでも「東京オリンピック中止」の可能性は1%未満か」.
So the possibility of cancellation of Tokyo Olympic (this year?) is estimated to be less than 1%.
And the author also states in the middle of article 「よほどのことがない限り、開催するでしょう。まさに「国家の威信にかけても」という感じですよね。」: The Olympic Game will be held unless something unusual happens. It is like a "on nation's pride".