Is it actually wrong to say "kasse af øl" or is this also acceptable?
Yes it would be wrong, you just say 'en kasse øl'.
'En kasse af øl' souds a bit like it's a box made from beer..:)
Same in German: Ein Kasten Bier.
Couldn't this be: "we drink. .. every Thursday"?
"Vi drikker ... hver torsdag."
No. PÅ indicates that it's the following Thursday.
Hvem drikker ,,crates of'' øl, og hvor kan jeg finder en?
They are very common.
Is box or crate better
For beer (and bottled drinks in general) "crate" is the better term.
Det er i dag!