Just wondering. I caught a Lv. 55 Quirky Male Croagunk. Would that affect it's stats?
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.
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.