How can I transfer all messages and accounts from Outlook Express to Eudora OSE?

They are both POP/IMAP clients. You simply point your Eudora OSE to the service that your Outlook Express was pointed to.
If your settings on OE were to delete the mail items from the source server than there is more to do as OE stores them in folders.
There is an Import tool. Click Tools | Import. Manually select which you want from Address Book, Mail, Settings, Filters. Don’t select the “Import Everything” as it leaves you hanging. Once you pick one option such as “Mail”, it will then let you choose the local client of Outlook Express.
More details would be helpful to understand the extent of your question if this doesn’t work for you.
Outlook Express is not available for Win7 or Vista and I rarely ran it to know how the export function worked. If you are still stuck, I can spin up a VM with XP on it and get Outlook Express.
Happy to help, but not sure where you are stuck.

Hi Thanks a lot. It is when I have to choose the local client of Outlook Express that I have problems… I do not know what to choose… Any idea?