A lot of what has been said already is all very likely. Although we have no way to know for sure what would happen, it’s fun to theorize so I’ll take a shot at it.
So, since Tony dies, that means that Hammer and Ivan (I think that’s his name, feel free to correct me) get what they want, I believe Ivan’s motivation was to have Tony dead, so he gets what he wants, Hammer’s motivation is to be a rival to Tony and try and make his own version of the Iron Man suit, and if Tony’s out of the picture then either his suits get taken by the government or by Hammer Industries, unless Stark Industries or Rhodey somehow stop this from happening.
The way after Thor is made pretty clear. Odin would likely leave Loki as ruler of Asgard, and Loki’s plan is to happen a lot sooner. This is unlikely to affect the events of GotG, but I honestly don’t know tbh.
I haven’t seen Incredible Hulk, so I have no idea how things there would be affected by Banner’s death.
Widow’s death might not have any impact, but there’s also a possibility that her family finds out about it, as unlikely as that might’ve been at the time
Barton’s family would likely have a funeral for him, and Kate wont ever become his successor, but otherwise his death doesn’t have any impact I think (which is honestly very sad but it is what it is)
Cap is still in the ice, as we are shown, and Marvel comes to help, so this likely means that Fury is putting together a new team as fast as possible to stop Loki. So this leaves one final question: what heroes are there to be a part of this team (besides Cap and Marvel, obviously)?
Well Spider-Man and Ant-Man are immediately out of the picture. Peter is still very much a kid in Iron Man 2, so he’s not even close to ready. I highly doubt that bc Hope is dead and Hank is arrested that Scott could possibly end up being Ant-Man.
The Guardians aren’t a thing yet, and most are busy doing whatever, so they aren’t any good, unless by some miracle Quill and Yondu get involved.
I assume Wanda and Pietro are both still in the custody of Hydra at this point, not sure, but there is a possibility they could end up on SHIELD’s radar and end up helping, but that’s not very likely.
T’Challa isn’t ready for the role of the Black Panther yet, however, T’Chaka currently is, so on another slim chance, he might help.
TL;DR
Bad guys get what they want, only Clint has a funeral (maybe Tony is missed, idk), and there’s a very slim chance that other people besides Carol and Cap are willing to help fight against Loki (however it could be enough to stop him)