Does 'ori' mean the same as 'sau'?
Yes, but it is much less used. I would stick to "sau".
What's the difference between sau and ori?
I'm not a native English speaker, but the English sentence can't be a question, can it? Shouldn't it be even in colloquial talking: ”Does the bear eat meat or vegetables?“
One can use only the tone of voice to indicate a question in English but it is much less common than using the "does the bear eat...?" construction. I expect it was used here as reminder of the common interrogative construction in Romanian.
But where is the interrogative sentence? Where is the auxiliary verb DOES?