The two monks I've played recently were drastically different both in terms of combat style and roleplay.
Pavlo was a martial artist monk/brawler fighter. He wasn't really a monk, I suppose, seeing as he wore armor and didn't have any supernatural powers. He was a dim-witted pugilist that liked using force to solve all of his problems. He was dressed in battle-torn and blood-splattered leather armor with the teeth of his enemies lining the knuckles of his gloves, a habit he started prior to the game when he was involved in the blood sports of his city.
The big bad of the game was someone who used ancient magic to ascend to power through nefarious means. Pavlo developed a hatred for 'secret magic' and started taking anti-mage feats. Such was his luck with saving throws and casters failing their defensive concentration rolls (Disruptive chain and high level Brawler ability) that he though himself immune to magic and capable of punching the magic out of people.
Inspiration for his voice and style was mostly derived from Rocky Balboa. Well, a caricature of the character that I distilled from the snippets of the movie I've seen. Addled from a lifetime of blows to the head in underground boxing matches, his speech was slurred and he said the most inane of things. Implacable friend, but his trust could easily be gained with some honeyed words or bountiful bosoms.
Denjiri was a maneuver master and Monk of the Lotus (GM allowed me to mix them despite Quivering Palm interacting). He had little but the robes on his back and his weapon. He fought with a kusarigama, though he only used the bladed end against non-humanoids. He hated bringing suffering to living creatures and primarily focused on making them unable to fight with trips, dirty maneuvers (flavored as striking pressure points), and Touch of Serenity. He tried to subdue and reform the wicked and misguided when at all possible.
Denjiri was originally a man driven to excess in drugs, gambling, and women. He developed a life-threatening illness and all of his former friends and gold fell away. Having nothing left, not even his health, he turned to the spiritual paths that he had always neglected and mocked before. A devout of Irori provided him aid and showed him a path of asceticism. After adopting a a radical set of dietary and spiritual practices he found that his illness had less of a hold on him, though it would resurface should he falter in his regimen.
He was loaded down with the monk vows. Despite being unable to pursue many earthly pleasures, he was very lighthearted and always had a joke or a song to keep spirits up. He was a priest of Irori by the time the game started and was always the first to bring up spiritual matters, praying for any that died or seemed to need guidance. He always placed the good of others above his own and spent most of the money he gained purchasing things for his friends, both NPC and PC. He was killed by a troll king when he closed on it in effort to save a fellow adventurer.
Didn't have any particular inspiration for Denjiri. I suppose the jovial traveling priest archetype was inspiration, though I can't pinpoint a particular character that I got it from.
I don't tend to see such eccentric monks in play with my groups. Then again, I'm usually only one that plays monks.