First of all the name of the Allfather is Óðinn - with a long 'o'. :-)

> It's not really an exception, but one of those general rules that modify
> everything with a certain pattern. I think it may even be covered in one
> of the lessons for this course, even though it's not complete. (I don't
> remember where I encountered it.)

True. This is in the incomplete lesson 8. But the discussion there is
short and (as I read it now) seems partly misleading.

> First of all, Oðinn (nominative singular) is stem Oðin + ending -n.
> The -n replaces -r because of a rule about stems ending in -n, -l, -s.

Correct.

> So the dative would seem to be Oðini. Except that hits another rule,
> which as a non-specialist I just see as "patterns like '-ðini' sound awkward".

That's not a bad rule. Havard worded it a more formal way.

Here are some singular declensions (nom. acc. dat. gen.):

hamarr (hammer)
hamar
hamri
hamars

jöfurr (lord)
jöfur
jöfri
jöfurs

jökull (glacier)
jökul
jökli
jökuls

Hamall (a proper name)
Hamal
Hamli
Hamals

spegill (mirror)
spegil
spegli
spegils

himinn (sky, heaven)
himin
himni
himins

jötunn (giant)
jötun
jötni
jötuns

aftann (evening)
aftan
aftni
aftans

As for the lines from Hávamál:

geiri undaðr [with] a spear wounded
ok gefinn Óðni and given [to] Óðinn
sjálfr mér sjálfum myself [to] me myself

I put within brackets the meaning denoted by the datives.

geiri: instrumental dative (as in latin: ablativus instrumentalis)
Óðni: dative proper
mér: dative proper
sjálfum: dative proper

What I mean here by 'dative proper' is that this dative denotes
someone on the receiving end of 'gefa; give'. I think the latin word
'dativus' is derived from the verb 'do' which means 'I give'. The Icelandic
name of the case is 'þágufall; acceptance case'. Remember, though, that
the Icelandic dative plays the roles of both the latin dative and the
latin ablative.

Kveðja,
Haukur