Font settings are a bit tricky in Thunderbird. Try these steps.

1) main menu bar

  View > Character Encoding > Auto-Detect > set to "Universal"

2) View > Message Body as > set to "plain text"

3) Tools > Options > Display > Formatting > set preferred default fonts and sizes

4) Tools > Options > Display > Formatting > Advanced

a) Western Page
set fonts and sizes as desired
tick "Allow messages to use other fonts"
tick "Use fixed width font for plain text messages"
Outgoing Mail UTF-8

	   Incoming Mail UTF-8

untick "When possible use the default character encoding in replies"

b) On "Fonts For" drop-down menu repeat the procedure for Unicode and Central European.

c) On "Fonts For" drop-down menu select "User Defined" and repeat the procedure.

This will cover most messages, but you may have to repeat this for any other character encodings that cause you problems. For example, messages in ISO 8859-7 will mean you have to change the "Greek" page too. If you don't know which character sets correspond to the Thunderbird pages they're all on Wikipedia and elsewhere.

5) Go to Tools > Options > Advanced > Config Editor

mailnews.force_charset_override false

6) Folder Properties

Default Character Encoding User Defined

Uncheck 'Apply default to all messages'.

Now æøå (the Danish characters) are all replaced by an small rectangle with F1 and two other letters in it. For step 4b Unicode didn't come as a choice possibility. Step 5: there was nothing in my Danish version that resembled Config Editor. (If instead of Advanced under Fonts I chose Advanced in the right hand top corner I got a threathening message of voiding the guarantee!) Step 6: I could not find a Danish equivalent for "Default Ch...User Defined" I have checked that all the other steps are taken.

For step 4b, please provide a screenshot.

http://support.mozilla.org/en-US/kb/how-do-i-create-screenshot-my-problem

"I got a threathening message of voiding the guarantee!"

You found the config editor.

6) Folder Properties

Right-click the folder - Properties

In the current Thunderbird release version (24.4.0) it's called 'Default Character Encoding'.
In the current Thunderbird beta (28.0) it's called 'Fallback Character Encoding'.

What version of Thunderbird are you using? I have no idea about what this is called in Danish.

Changing "mailnews...override" to false seems to have solved the problem, judging from some of the hitherto wrong mails still in my In-box. I even managed to revive some html-mails by changing step 2 to html. Now there is probably no need for a screenshot for step 4b. I use Thunderbird 24.4.0. Step 6 in "Danish" says Standard Character Coding and is set at User defined. It also solved the problem that prints of emails that I had corrected on the screen with changing it to Unicode still came out with gibberish. Thank you very much for your help. A long standing source of irritation appears overcome.