Can I resign players even if it puts me over the current season salary cap after I've been eliminated for the season if I have cap room for the next season?

You still have to be under the cap during each postseason game stage, regardless of whether you are playing.

So if I'm tight to the cap this stage and have 40 mil for the offseason, first chance I can re-sign is end of season stage?

You can cut players down to 45 if you need to, also you may be able to re-sign some guys with 75% bonus and get your cap number down.

well you can resign a player during the regular season , during the playoffs or you can wait until the day before end of the season stage to do it

Me personally I always do the resigning of the players after the championship game has been played unless the league title game is later that day then I do it before it is played.

Awhile I do the coaches during the regular season.

that way I don't have to do both at the same time.