If Ser Osmund Kettleblack was a defending character in a challenge could a player, during his actions, use a Kingsguard Squire to stand him and have Osmund give himself +4 strength?

I believe so, changing from kneeling to standing does not remove the character from the challenge so the squire can stand him without issue. Ser Osmund would still be defending and his ability only checks that the character is defending.

I await any of the far more knowledgeable people to correct my understanding of the rules

Yes, you can absolutely do this. I'm not sure why you'd think you couldn't, except if you thought that standing a character removed them from a challenge (which it doesn't).

radiskull said:

Not here, though. AGoT: Dare to be different!

For which we love it.