Word Choice – Difference Between ‘The Meeting is/has Finished’ and ‘Meeting Over’ or ‘Meeting Done’

I'd say the phrase 'one-on-one meeting' sounds much more natural.

The term 'one-to-one' is more often used in the with any of the following:

• one-to-one relationship
• one-to-one function
• one-to-one mapping

Yes, there is a difference. One usually doesn't have a meeting "over" something, without using more words. For instance,

"All the employees at SEI Corporation are invited to the meeting where we will go over the new internal communications system that the company is about to bring in."

You are correct, however, that "over" can also mean "about something," as in this example:

We argued over who would do the dishes.

So why wouldn't we say, "We had a meeting over who would do the dishes"? It is largely idiomatic, but to a native English speaker it would sound odd.

A better choice than either "on" or "over" in the original example would be "about," except that it is used later in the same sentence. The sentence could be rephrased to use "about" like this (changing the second instance to "going"):

"All the employees at SEI Corporation are invited to the meeting about the new internal communications system that the company is going to bring in."