Just wondering. I caught a Lv. 55 Quirky Male Croagunk. Would that affect it's stats?
NO, it would not, same with Hardy, Docile, Bashful and Serious.
Quirky nature is a neutral nature so that means it does not increase or decrease stats in any way.
No, as the Quirky Nature both Increases and Decreases the Special Defense Stat by 10%, resulting in a net gain of 0 (nothing xD).
Quirky Nature itself will not, but the Pokemon's characteristics ("likes to run" etc.) will affect it's base stats.