This is actually a question I've wanted to ask in the other direction. I say 'Oh well' a lot after another sentence, usually to express disappointment, resignation, or futility, like a shrug or a sigh, sometimes more or less cheerful, sometimes not. But I'm not sure 'Na ja' really conveys the same thing in German.
Rats, I forgot to stop for groceries. Oh well, there's always canned soup.
We worked so hard on that proposal, and then the client didn't like it at all. Oh well, we gave it our best shot.
In that case it's usually on a falling pitch: Óh well.
When it's more cheerful or ironic, said with a wink or a grin, the pitch rises first, then falls: Óh, wé-ell.
What, you mean I didn't win a million dollars in the lottery? Oh well, such is life.
So he thinks the boss is going to choose him even though he totally messed up the last two projects? Oh well, I guess the rest of us don't even need to apply, then, do we?