No, they don't.
"Osoroi" means like "a pair of" or "matching".
If you find someone's umbrella same or very similar to yours, you can say "Osoroi dane".
So, you can use it if you see any affinities or resemblances.
"Oniai" is one of words to commend some things for their fitness or suitability, I might say.
If your friend puts on a cool cap and if it seems to fit very much to him, you can say to him "Oniai dane".
Also, a loving couple would be described as "Oniai no couple."
In other words, "osoroi" is based on some facts or objective things while "oniai" expresses someone's opinion or subjective point of view.