What are the rules for a creature moving through a space made for a creature smaller than them. For example, a human trying to move through a house made for a halfling or an ogre running down the thin corridor of a castle.

A creature can move through a space meant for something one size smaller than they are. They move at half speed doing it. 

Plus they may need an athletics check if they get themselves stuck. When in doubt brute force.

Squeezing into a Smaller Space

A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that's only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it's in the smaller space.