You can use any EM to do this and connect to an MSDE instance. The triggers are stored in the database, so a backup and restore will move those.
I didn't think DTS packages could exist in MSDE. If they are, then you need to "open" them and save them on the new server or save them a structured storage files in the file system and copy them over. They can be run from the filesystem or you can load them back into msdb on the new server.