What are common strategies/considerations for controlling distortion in an op amp given a 20-20K (Audio) frequency spectrum?
Are there inherent non-linear/distortion characteristics of an op-amp?
Yes. Bare opamps are actually quite non-linear, or at least their linearity can't be counted on much.
Or is this all contingent on implementation?
No, since you're asking about opamps, not the circuits around them. The opamp is still a opamp regardless of what you put around it.
What are the tried and true techniques for minimizing distortion in an op-amp?
I don't know since I'm not a chip designer.
Minimizing distortion in the overall circuit that includes a opamp is usually done with negative feedback.
You have now completely changed your question, asking about opamp circuits instead of the opamps directly. That really should be a separate question, but since I'm here, I'll address it at least a little.
As I mentioned briefly above, quite linear circuits are created with opamps by using negative feedback around them. The very high gain of opamps contributes to making them non-linear in the first place, but it also allows for feedback to get good linearity at modest gains.
I go into the math behind negative feedback in detail here.
When they say, that the opamp has high gain, they say nothing. You must understand that the gain is so high, that for any not saturated output the input is practically zero, and for any input different from practical zero the output would be much higher than power source voltage, so in fact it just reaches the maximum and gets saturaded.
Of course in real life it's a bit different, but for most cases these are the rules.
So if you are calculating simple circuits, and you see negative feedback, just know, that difference between plus and minus inputs is zero: because you know, the output is not always saturated.
Similarly, if you know for sure that the inputa are very different (taje opamp in comparator mode for example), the output can only be VDD or VSS.
On other hand, when they say that linearity is better- well, it's better beyond compare, but the gain is from other league.
It might help to know what you are doing. However, a rule of thumb is that you need at least 10 times more open-loop gain than the closed-loop gain at thr frequency you are working at. In other words, if you want to multiply a 1000 Hz signal by 10X, your opamp needs an open-loop gain of at least 100 for "reasonably" low distortion (or gain error). More is better.