The only thing you can do is manually manage music. If you sync, it will erase everything first, because syncing music files from multiple computers is not allowed.
Manually managing music means you have to drag and drop from within iTunes any time you want to put music on it. There's a checkbox in the summary screen to enable that, then you click Apply. Click and drag a playlist from the sidebar up to the iPod to add it, click and drag a song from the library to the iPod to add just a song. To delete a song or playlist, you can delete it from the iPod music app itself (swipe across it in the list of playlists or songs, tap Delete). To delete it from the iPod using iTunes, first get to the iPod Music window in the sidebar. The main window should then have the list of songs that are on it, and the toolbar at the bottom will have options like Autofill and Settings. Select the songs to delete, and then hit Delete (or Edit -> Delete, or right-click and delete).
