@nyuwa
Strawberry supports saving playlists with relative paths,
Go to Tools / Settings / Playlist and select "Relative" or "Ask when saving" under "When saving a playlist, file paths should be".
When you save the playlist in d:\music, the paths should then point to directories / files without d:\music.
This way you can copy the playlist files over on the other computer to the same music directory on a different drive.
Another option is to simply edit the playlist file in a text editor and do a find/replace of d:\ with e:\