I'm wondering if there's evidence of people using these kinds of everyday phrases in these cultures, or whether it's something specific to modern religious societies.
Using expressions like "by the gods!" was definitely common in Greece. It could be used seriously (like, in Plato's account of Socrates' trial, Meletus responds to a question by saying "I swear by Zeus..."), but, as an example, take a look at Aristophanes' comedy, The Clouds, it's full of the sort of thing it sounds like you're looking for.
"Great gods! will these nights never end? will daylight never come? I heard the cock crow long ago and my slaves are snoring still!"
"Ah! great Zeus! what a brain! what subtlety!"
"By great Zeus! by all the gods! you shall not scoff at me with impunity!"
I don't know about Nordic languages, but Greek and Latin had their share of expressions mentioning the gods (or demi-gods) and they were very commonly used.
Check out this (very old) paper on the usage of mild oaths in the plays of Plautus and Terence. Hercle or Meherc(u)le, Ecastor or Mecastor, Pol or Edepol were mentions of Hercules, Castor and Pollux respectively and widely used as interjections in everyday language.