So basically I'm gonna ask: Is it even worth it to try and make sense of technological development in the Fallout world? I mean at first it was all straight-forward: US had bio-weapons, robots, nuclear shelters, survival stuff like GECK or water chip and most of this tech survived through vaults, the BoS, and the Enclave, with the Enclave being the only ones to advance technology. Then Tactics came and garbled things up with super advanced robots, then came Fallout 3 which added the MIT as a seriously technologically advanced group and then New Vegas blew it even more out of proportion with the Think Tank tech. It's especially confusing when it's implied that most of Big MT's stupidly advanced tech is pre-war like the Dead Money vending machines, or that the Tactics robots were made but then disappeared into thin air with no trace of them anywhere but Vault 0. Let's not even delve into FEV here.

The institute is quite possible since we know MIT is one of the premiere places to learn about technology in the world so it is plausible that they continued to teach their children about technology and they continued to advance on Technology.

I have not played the DLC's yet for New Vegas so I can not really comment on the Big MT.

I wouldn't consider the robots in Fallout Tactics to be "super advanced" they just don't have that "1950s" look that IMO Bethesda focused on more so then the originals. Not saying it is a bad thing. Just that Bethesda really drove home the 1950s aesthetics. So it is somewhat unfair to look back at past games and complain that they aren't 1950s looking enough.

As for Enclave, Think Tank and Commonwealth tech. We can use "it is tech that advanced after the Great War." To explain it. People took tech that was new before the Great War and built upon it afterwards.

Tech before the Great War just developed differently then our own. I don't think it's something that developers of Fallout ever thought people would look into and try to explain. It just is. Technology continued to use vacuum tubes and so on and yet people managed to created AI machines with it.