When a player is eliminated, can they still talk and discuss strategy on the table or do they have to stay silent?
The rules don't explicitly cover this, so we must use our own judgement.
When a player dies, they reveal their role and their cards. The dead player has no more hidden information. Therefore, I see no reason why they should be required to remain silent. Additionally, one could argue that they aren't even playing the game any longer, and therefore can't possibly be bound by its rules. (In before someone comments that some Bang! character I don't know about can revive.)
If your play group really has an issue with dead players influencing opinions after death, then introduce a house rule. Dead players can't speak (at least about the game).
Is there rule for table talk?
Q1. Can players talk during the game?
A. Of course! That's one of the most amusing aspects of the game. --
but even there nothing is said explicitly about dead players. This means that the decision must be made between the players (a house rule).
But does it matter?
Normally: No. It should not matter if the dead players can talk. (Except if you let them see other players' playing/role cards)
When playing with the tournament points system (BGG, Wikipedia, Bang.cz): Yes, it matters. Also the dead players may get points, and therefore it is fair to give the players opportunity to affect the outcome (and their score) by talking. This game is very much a social game, where bluffing and manipulation has a huge role.