The main rulebook says you must check for stress before you perform an action during the Activation Phase. If you can take an action at some other point in the turn, like from Pilot Lando or Squad Leader, does having a stress token make you unable to take those actions?

If you are stressed, you can't take any action, even a free one from another source like Lando or Squad Leader. See page 17 of the Rulebook.

While a ship has at least one stress token, it cannot execute red maneuvers or perform any actions (even free actions).

You can however, have someone give you a token (like target lock, or focus), just so long as they're not giving you the action.