Does this mean around the inside of the house or around the outside of the house?
Around the outside of the house. If you are referring to the inside of the house, you would usually say 'Caută prin casă'.
I think you would have to be more specific; e.g., "Căuta în interiorul (inside) "în afara" (outside) casei!"
A lot of these are clearly nouns rather than prepositions in Romanian, and we could probably translate them all with similar phrases (Search the outside of the house), but it is quite interesting how Romanian prefers this sort of construction.
In Romanian, împrejurul is actually a preposition, even if it looks like a definite noun. In the sentence, it specifies WHERE you search, not what you search.
Cauta = search. Search around the house
I tried to get closer to the grammatical form - offering they search the surroundings of the house. DL didn't like it.