There is a toolbar at the top of the playlist pane. Look for "Save Playlist" and "Load Playlist". Clicking "Save Playlist" will allow you to save the playlist as a .pls file to whatever folder you choose. When you want to call up that particular playlist, you can click "Load Playlist". Select the playlist you saved previously and it will open in a new tab on the right of the tab row. (Note: Focus does not automatically jump to the newly opened playlist; you have to select it.)
It appears to retain the original track order. If you alter the playlist, just save it again and overwrite the previous one; or give it a different name and save it separately. Dynamic updating, I don't believe is possible in Strawberry.