How do you move your team from feeling overloaded to feeling empowered?

Clear objectives and metrics of success along with offering help to prioritize.

They should be owners of their own processes with a CLEAR picture of their contribution to the whole outcome. When staff is empowered as the owner of the process they interact with , they get to develop a sense of belonging that in my experience translates into innovation and efficiency. 

A true accountability culture.  This is easy to say and notoriously hard to actualize.  I've seen many organizations full of smart people who want the responsibility but not the accountability when things don't go according to. This is a culture shift that involves clear R&Rs, direct line of sight into how each person's goals and actions ladder up to the bigger picture, a feedback-rich environment, psychological safety to fail and learn rather than hide your mistakes, and enterprise mindset.  Empowerment comes from the clarity to act, not just in the big moments but it the tens of thousands of decisions made every day on the job by every employee, and a culture that celebrates the learnings, no matter win or lose.

Something that has proven to be helpful in my experience is connecting the dots so each member of a team is able to understand the full cycle of the processes they interact with. When the team is able to understand how their big -or small piece- of the puzzle fits into the bigger picture, they can recognize their impact and that leads, more often than not, to empowerment. (assuming there is personal alignment with the mission and a supportive culture)

Identify what group of activities to stop ASAP in alignment with organisational strategies. Make sure your team know that you have their back and lead by example of not working excessive hours and maintaining a good worklife balance.

I must note, some personnel work with prioritisation well, others will just keep going until they break. So a variety of methods is likely required to achieve a successful outcome.