お風呂(おふろ)-- bath
まい is a mistake; it should be 前 (まえ), meaning "before."
後(あと)-- after
入った(はいった)from 入る(はいる)meaning "enter."
I'm pretty sure おふろに まえに べんきょうを します is grammatically wrong. The version with の is right. However, I get the sense that there should have been a はいる in there. In that case, おふろに はいる まえに べんきょうを する is perfectly legitimate.
The sentences mean (1) "I (will) study before my bath," (2) "I (will) study before I take a bath," (that's if it's supposed to have はいる in it), (3) "I (will) watch TV after my bath," (4) "I (will) watch TV after I've taken a bath."