Old MS Outlook Express for Mac copy/export/move
Your question doesn't specify how you want to be able to view/store them, but I can think of a few options. Unfortunately, MS Outlook Express for Mac 4.01 doesn't offer any export option, so these are all workarounds.

Backup the actual data

Before doing anything else you should backup the actual data. I'm going to assume everything is in its default location, but if not this should be enough for you to locate where the data is.


Double-click on the Macintosh HD icon on your desktop
You should see an Internet folder - open this folder
Now you should see an Internet Applications folder - open this folder
You should now see the Outlook Express folder - open this folder
You should now see an OE Users(s) folder - open this folder
Now you'll see a Main User folder - open this folder
Now you'll see an Internet Mail folder - this is the folder that contains all your email data, including Inbox, Sent Items, etc.
Copy this folder onto another disk 


Now that you've got the actual mail data backed up, it's time to look at a number of options.

Manually drag &amp; copy the emails you want

One option you have is to select all the relevant emails, drag them into a folder on your iMac's desktop, and then transfer them to be read with MS Outlook for Mac. To do this:


Create a folder on your old iMac's desktop
Open Outlook Express
Select the emails you want to keep (or you could just select all)
Use your mouse to drag them all into the folder you created at Step 1
Open the folder to check that you now have x number of files in there (there should be one for each email)
Now you need to transfer that folder on to your newer Mac. Probably the easiest way to do this is to copy the folder onto a USB flash drive and then transfer them via the drive onto your newer Mac. However, depending on your setup, you may have other options open to you.


Once you've copied the folder onto your newer Mac, you can open it using MS Outlook. Depending on the version you have, you may need to drag an individual email onto the Outlook icon on your Dock in order to view it.

Using various apps as a go-between to view emails in Apple Mail

If you're wanting to access these old emails in Apple Mail, one option may be to use others apps as go-betweens to try to get the data into Apple Mail. However, this may be a hit/miss exercise. By way of example, one way this could work is to do as follows:


Download Outlook Express 5 to install on your old iMac
Download Eudora 5 to install on your old iMac
Use Outlook Express 5 to import your emails from Outlook Express 4
Use Eudora to import the email from Outlook Express 5
Transfer the Eudora data to your newer Mac
Use Apple Mail to try and import mail from Eudora


The above is not a step-by-step guide, just a broad summary. As you can see though, it requires a lot of importing data into various formats and may or may not get you to your end goal.

Save your emails as PDFs

This option is probably a good one in that you can view them on any device and choose to combine them as one PDF, or make a book, etc from them.

Probably the easiest way to do this is to download an old version of Adobe Acrobat to install on your old iMac and use that to save each of the emails as PDFs. You can then transfer the PDFs to your newer device.

Another option is to do this after you've transferred the emails to your newer computer via one of the above methods.

Save your emails as Text

This option is another good way to go, because like PDFs you can view them on any device. In fact, you can do this directly from Outlook Express as follows:


Create a folder on your old iMac's desktop
Open Outlook Express
Select one of the emails you want to keep
Go to File > Save As
In the Format drop-down menu, select SimpleText Text Document
Navigate to the folder you created at Step 1
Click on the Save button
Repeat Steps 3 to 7 for each email you want to keep
Now you need to transfer that folder on to your newer Mac (e.g. using a USB flash drive)


Once you've done this they will each open in TextEdit (or another similar app if you're using Windows etc). Once there you can print, save as PDF, etc.