"Our house is full of people."
Translation:Nia domo estas plena je homoj.
"je" is very often defined as "used when no other preposition is suitable." This is pretty much straight from the Fundamento and doesn't reflect the much clearer actual usage that quickly developed.
Also, a "je" phrase can always be turned into an accusative phrase without "je" (from the fundamento).
PIV, fortunately, has a better set of definitions.
1 - supplement to a quality, an object associated with an adjective that explains "how" to be that way. The meaning is specific to the adjective. "full OF" "apart FROM" "lucky AT" "content WITH" - Sometimes "de" / "pri" / "al" / "ĉe".
2 - (synonym "de") a similar supplement to a noun showing an action or condition. "a right TO" "a thirst FOR" "a belief IN"
3 - (often accusative) precise time. "ON the third day" "AT three" (je la tria / la trian)
4 - body-part that an action connects to (take BY the hand) or a similar relation (the shipwrecked one clung TO a board)
5 - (often accusative) measurements of qualities or differences. "taller BY half a head" "older BY a year" "(BY) a three day's journey distant"
6 - miscellaneous adjuncts to verbs, similar to 1 and 2, that have meaning specific to that verb. "be ill WITH" "suffer FROM" "believe IN" "wager AGAINST" "change TO"
Not really, "per" means "by means of" so it wouldn't tell you that the house is filled by people, it tells you that people were the means by which the house was filled (and the thing that fills it may or may not be people). So while the house is full (of something unspecified) "per" only tells us that is was by means of people that the house became filled. Ekz. "La domo estas plena de katoj per homoj." In this example, I have added in "de katoj". The house is filled with cats, but it was people that put the cats there. I hope that helps.