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.
Hvem drikker ,,crates of'' øl, og hvor kan jeg finder en?
They are very common.
Couldn't this be: "we drink. .. every Thursday"?
No. PÅ indicates that it's the following Thursday.
"Vi drikker ... hver torsdag."
Det er i dag!
Is box or crate better
For beer (and bottled drinks in general) "crate" is the better term.