Strong as he was he could beat his opponent.
I saw the above sentence on a website which explains the usage of inversion. It gives the previous example. Is this equal to:
Though he was strong he could not beat his opponent.
No, the the two sentences you list are not equivalent. The meaning of the first sentence is actually "because he was very strong, he was able to defeat his opponent".
I looked up the source of the quote, and I suspect that the author of the article made a typo in that sentence because the rest of their examples make sense but this one does not.
The proper equivalent to the second sentence would be:
Strong as he was, he could not beat his opponent.
This has the negation, which the example sentence they give does not.