"In" is just more general. Think of this sentence as talking about this person's lack of effort "at home" in general, which may refer to an apartment, condo, actual house, mansion, etc. "Nella casa," is would refer to a specific house where this guy isn't doing any work.
Because your translation could mean something else. In a specific context, the meaning could be the same, but word for word it is a different meaning. Aiuta is the verb in the sentence, which refers to actually action of helping, not the noun version of 'help'.
In other words, 'He is no help in the house' could also mean that he's bad at housework, rather than being unwilling or unable to do the work.
“are” verbs such as this one (aiutare) typically conjugate lei/lui with an “a”: aiutA, mangiA etc “ere” and “ire” verbs conjugate lei/lui with an “e”: leggE, bevE etc
they also differ in the loro conjugations. “are” verbs are loro aiutANO mangiANO. while “ere” and “ire” verbs are loro leggONO bevONO