Check engine light turned on with code P2096, what does the code mean?

That code means the exhaust is too lean after the converter. The only way to see what it really is would be to put a scan tool on it and watch the rear sensors response along with the front sensor. I have seen exhaust leaks cause it, also have seen it on cars with a bunch of modifications.

It could be either of the items you have been told as well, but without a good scan tool in the hands of someone who knows how to use it, you could spend a lot of money and still not solve the problem.