One thing Beren did do by himself was get through the Ered Gorgoroth, and that was no picnic. Shelob lived there, and many other monsters older than the sun,n, and the whole area was tainted by Sauron's sorcery, so probably full of undead abominations.
in all of Tolkien's books, I think that was the only oath that was sworn on Eru.
Not quite. Unfinished Tales says that when Cirion and Eorl swore alliance, Cirion put his oath in the keeping of the Valar, 'and of the One who is above all thrones for ever,' which was the first such oath since ELendil swore alliance with Gil-galad.
You know, this made me think about something I never had before: who was it that brought the Nauglamir and Silmaril to Dior from the Land of the Dead that Live? Presumably a Green Elf from Luthien and Beren's household, but man, you wonder what their story was. The most precious object in all of Arda, the greatest work of Dwarf and Elf combined, holding the untainted light of the Trees. Something that provoked desire in all that looked upon it, for which kings had been slaughtered and realms broken. Of all the elven-realms that once stood only Gondolin still stands unbroken, Morgoth reigns over nearly all, it's a dark and dangerous world between Tol Galen and Doriath. Plus he surviving sons of Feanor are still out there with the oath that will drive them to kill you if you don't turn over the Silmaril.
But some no-name Laiquendi apparently picked it up and resisted all impulse and was bad-ass enough to make it safely to Doriath to hand it over to Dior.