Is it most likely or likeliest?

"likeliest" and "the most likely" are both correct and mean the same thing. As with most synonyms, you would pick between them based on the rhythm and structure of the sentence you're building. Without specific examples, I can't give more advice.

What is example of very likely?

It is very likely that the problem is in the thousands. It is very likely that more new political parties will emerge. It is very likely that it will be 5-4, So it is very likely that this series originated after 1948.