When playing a 5 or more player game of Twilight Imperium and someone is completely removed from the game, do you revert to picking two strategy cards each as per a 4 player game?
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No, nothing changes. The TI3 FAQ puts it fairly straightforwardly on the left hand side of page 2:
Once a player's eliminated, everyone plays by the same rules as they have been the whole game. You don't revert to rules for the current lower number of players.
As far as I know, a player cannot be eliminated from the game. He can lose all of his plastic figures, but still after each round he participates in the strategy- and action card distribution, by which he can affect the gameplay.
Conclusion from this would be that if the house wants to enable dropping a player, then it's house-rules specific.