Do you think Data and Odo would get along? How do Odo's strength, height, weight, intelligence, and calculating speed compare to Data's?
I think they would find each other unremarkable at first, then have a frank discussion on observing humanoids and part ways.
I could see Odo and Data having a cynical conversation when Odo starts remarking on human short comings and Data defends them. Beyond their variations on being the observer of the human condition though, I don't think they'd have much outside the line of duty to say to one another.
Odo only really has three interests. Kira Nerys, reuniting with his people, and enforcing the law. Data doesn't really factor into any of those. I can't really see the conversation even starting.
Data basically gets along with everyone. Although, I admit, if you stuck the two in a long shuttle ride together, I have a feeling it would be a quiet journey...
I never got the impression that Odo was especially intelligent. Not dumb and perhaps above average, but certainly unremarkable compared to Data. And is his strength above average? He certainly knows how to handle himself in a fight and his shape shifting gives him some unique advantages, but have we seen him exhibit strength above and beyond the norm?
Data could tell Odo about the time he attempted to kill Kivas Fajo, and Odo could offer his input as to the moral and law enforcement ramifications of Data's actions and attempted actions. Data: "What would you have done?" Odo: "That's a good question."
Using your arms, shapeshifting or no, to stop a turbolift from falling by warping it out of shape to jam the shaft seems like a display of strength above the norm.
Odo was essentially a conflicted man but Data isn't; I don't think they would relate but OTOH, maybe Data's 'want' to be human and Odo's life with solids has a commonality
I'm sure he turned into one whenever Quark had a calculator nearby while making a deal with the smuggler of the week.
Well Odo was in a similar situation when Tain and Garak captured him. We'll never know for sure given Garak had his anti-shape shifter machine, but I was under the distinct impression Odo was about to give him a beating. Mind you it would probably be just to the point of unconsciousness, and Odo did save Garak's life despite it all. Really though, Odo had a demonstrated behavior of putting his own sense of justice before letter of the law and morality. He had no problem working as the literal equivalent of a Gestapo agent during the occupation. In fact he often pines on how those were the good old days when everything was kept secure. He often chafes at Federation due process, he'll lock Quark up without charges our representation regularly, he wanted to break up Rom's union because he thought they were bad for public order, and he offered to arrest a bunch of Paigh wraith cultists who were peacefully chanting just because they bothered his girl friend. Quark was fairly accurate in calling him a fascist. So no, I really don't think Odo would've held it against Data for shooting Fajo who was a known criminal, even if he couldn't prove it.
I'm sure Odo would have been somewhat antagonistic towards Data upon first meeting him but the two would have worked out as a team when all was said and done.
Data would leave Odo alone. They'd get along fabulously. If they can get past Data's speech about how Odo mimicks the very thing that he seeks.
Picard and Janeway would order Worf and Tuvok to shoot them on the spot if they felt trapped in ten forward with those two doing a duet.