Which word doesn t belong?

I back your judgement in choosing 'hence' as the odd one out.
All the others are about a 'reason' for something or a condition that exists.
'Hence' is about an outcome or conclusion or a consequence.
Because it was raining, he took an umbrella.
Due to the rain, he took an umbrella.
Since it was raining, he took an umbrella.
It was raining, hence he took an umbrella.

Look the words up in the dictionary. Hence means afterward.

Hence=Therefore (indicates a RESULT follows)
The others indicate a CAUSE will follow.

I was hungry. HENCE, I ate lunch.
I ate lunch BECAUSE I was hungry.

I would choose "due to" because the others all need a clause, and "due to" needs just a noun. Due to the rain....Because it was raining, since it was raining, etc.

(Blank) it is raining, I'll stay home.
Hence does not fit in the blank. The others do