Intelligence is manifested in how one thinks: how one views problems, and how one solves them. Eliezer Yudkowsky, author of Harry Potter and the Methods of Rationality, explains his approach to the problem of very intelligent characters in this blogpost.
As a brief example, an intelligent character might take a look at what another character is doing, and go
It would be easier to do it this way
It's a very common trope to have an intelligent character take a look at something that's been done a particular way for a long time, and find a better way to do it - a way that makes perfect sense once its been shown. A famous example appears in Ender's Game, with Ender's "3D thinking" and "the enemy gate is down".
This comes through in dialogue. The intelligent character wouldn't be just accepting new information. He'd be asking "how", "why" - he'd be actively processing, challenging, figuring out how it all fits together. He'd be the one connecting the dots or spotting contradictions.
It might be that an intelligent character would arrive at an "obvious" conclusion, and then have to explain to "slower" characters the steps he took to reach it. Sherlock Holmes is built around this trope.
Vocabulary is not directly related to intelligence. Proper grammar and rich vocabulary are tied to level of education rather than to intelligence. While a university professor is not likely to be stupid, not every intelligent person is a university professor. That said, since your characters are A.Is, it's likely they have access to an inbuilt dictionary. Combined with intelligence, that would mean they wouldn't be making mistakes, with either grammar or vocabulary, and they'd be using the precise word for each situation rather than more general terms. That would result in speech that's very concise, very efficient. (Again, however, this element is not derived from the fact that the characters are intelligent, but from the fact that they're intelligent and they're computers.)