I'm thinking we'll probably get cameos, or at the very most a guest spot on the team for missions that involve them. I can see ways that the core four could easily have been major characters again in the third game, had it not been for the fact that they can be dead going into ME3. I especially expect to see Tali/Legion
and Jacob/Miranda play a significant part if alive in those two
expected plot points. Garrus is harder to place into the current
existing information about him.
I'm thinking we may get to see Garrus in some form on a turian world. I'm hoping he'll lose a bit of the crazy vigilantism edges he fell into in the second game and return to a different job within his home society. Though thinking about the threat of the Reapers and his actions in the first games this resolution would feel a little forced without a secondary reason, particularly if you romanced him. Honestly, I have the hardest time coming up for something reasonable for Garrus; he feels inextricably stuck to my paragon female shepard character who had no romantic partner in ME1. We don't know about his family and turian customs as far as I know, but it would feel like a reach when he's already forsaken about everything for shepard. I'm very scared that he's going to get killed off in some fasion early in the game if he's not already dead going into ME3
Tali would appear either as an exile or admiral as part of the negotiation for settling the dispute between the Geth and Quarians, probably resulting in the Quarians getting their homeworld back. A form of Legion would probably be in here as well. How is BioWare going to handle the possiblity of Tali being exiled to the Normandy OR being dead?
Then maybe we'll get to see Jacob/Miranda as part of an Earth or sol colony/base mission, that settles the differences with the Illusive man and resolves the choice at the end of ME2.
As for the minor and dying squad characters:
We may get a cameo of Thane on his deathbed, but I don't know, lung diseases are kind of iffy for touching last moments. I'm guessing if the age of 50 thrown around for Mordin is accurate he's going down around the same time as Thane (I have trouble believing the age) and have a similar cameo early in the game that varies depending on your ME2 status. Honestly Grunt is probably fine with a cameo for the big battle. Maybe I'm weird but I didn't feel all that attached to him. He's born from a tank and finds his place in Krogan society, great. He'll probably return to it in between the action of the first two games. Jack is so unpredictable it's pretty easy to write her whereever the devs want. As for Samara/Morinth, I have no idea. It really would depend on where the plot goes and what modules they have planned. I would be surprised if the DLC characters do anything more than a quick cameo and drop a handful of lines.
Final notes:
Maybe it's because I like them so much, but Tali and Garrus are really hard for me to write off the Normandy without something serious happening to either them or Shepard. Maybe they'll just be around like the crew in ME2 and have a conversation tree with a subsection that only exists if you romanced them in the previous game. I'm assuming the Cerberus crew is getting axed regardless of the outcome of ME2, maybe the old characters who played an active role in maintaining the ship (Tali, Garrus, Mordin, Jacob, and Miranda) will stick around in the role of the crewmates of ME2 and be replaced if dead by some unknown second option when dead? I think Tali's window of opportunity to become the new admiral will pass because of the suicide mission regardless, so she could be on the ship no matter the outcome. Mordin already passed his clinic on and is ancient by Salarian standards; he's probably fine staying on the Normany until he dies. Chakas, Joker and EDI could probably stay on the ship as well.
tl;dr:
It's hard to say what approach is realistic for living imports to ME3 without knowing the timing of the third act. The sooner it happens, the more I see a cameo for minor characters, keep major characters (Garrus, Tali, Mordin, Jacob, and Miranda) on the ship with Joker, Chakas, and EDI. If there's a significant delay in the beginning of the third act because of whatever reason, then I expect the crew to split again and to have guest missions with Garrus, Tali/Legion, and Miranda/Jacob on a turian world, the quarian homeworld and earth/sol.