Igor is the supporting sidekick of Lockjaw and assistant to Finklestein throughout the story. Igor will not be with Lockjaw when he leaves the lab, so he will have a bigger role in the beginning than he will later on, though it doesn't mean he won't be important. 

In the movie, Igor had an extremely small role. He spoke 3 words and was there only to bring the plans. Igor had a slightly bigger role in the game, Oogie's Revenge, but it wasn't much bigger. Being purely a joke character in the Nightmare universe, it's hard to make a proper character for him.

Igor will be an awkward, joyous, faithful lackey. He befriends Lockjaw, as he is supposed to be the one to watch over him with Sally. Igor never pushes a task aside and will do his best to find a way to complete it. He is the kind of monster you feel uncomfortable to be around, but enjoy the company of anyways. He never calls Dr. Finklestein anything other than Master in order to keep his never-ending streak of trustworthy-ness. Faithful and happy, Igor will go great lengths to please his master and receive his bone biscuits. He is an inventor, but never seems to show his inventions off. He fears Dr. Finklestein will make a far superior invention of the same nature. So he's smart enough to keep quiet when he needs to.

His voice should be raspy, yet smooth. Igor has that speech impediment which basically makes any 'S' of a word 'Shhhh'. (Planshh for example). His voice is gravely, but is not overwhelming. Igor speaks in third-person.

REFERENCE
------------------
https://www.youtube.com/watch?v=fb1Pnc3Y1sQ

https://youtu.be/9XQ6QBBOrJk?t=93

http://disney.wikia.com/wiki/Igor_(The_Nightmare_Before_Christmas)

http://the-nightmare-before-christmas.wikia.com/wiki/Igor