Thunderbird has an excellent import function to import mail from Outlook or Eudora. Due to a bug in Eudora there is a possibility your mail attachments do not get imported into Thunderbird. Here is how you can overcome this.
Eudora stores it's mail attachments to the folder attach within the Eudora data directory, e.g. c:\eudora\attach. During that process, it stores the path to the attachment in the mail header to later be able to access the attachment.
Thunderbird stores all messages and attachments of a folder within the mail system to a file of the same name within a directory structure reflecting the folder structure of the mail system, e.g. d:\thunderbird\Data\profile\Mail, if you are using the portable version of Thunderbird (which is strongly recommendable).
Eudora stores the full path of the mail directory into the header of the respective mail. If you move the entire Eudora data directory to a different location on your harddisk, these path's do not get updated (they should actually be stored relative to the Eudora data directory). For example, if you started using Eudora with p:\eudora as it's data directory and later move all the data to i:\eudora\private, the following effects will occur:
If the path indicated is on the same drive:
If the path indicated is on a different drive:
If you moved the Eudora data directory more than once over the period you used Eudora, you need to repeat these steps for every location where the data directory resided in the past.
Example: