Oswald is a Lumon employee working in Optics and Design. He works with Burt.
Oswald was referenced by Burt, just once:
Milchick: I have something for you.
Burt: The missing 7199-G. Oswald will be so delighted. I, too, am delighted.Season 1, Episode 7, Defiant Jazz (12:38)
Nothing else is known about him, though he may be involved in the production, distribution, or usage of the Ideographic Cards.