(あい) Pure love – usually two-way.
(れんあい) Love or relationships in general – that is to say, if there’s an ad for fortune-telling that says, “Test your luck in money! Love! and health!” it’ll be using 恋愛. If there’s an article in a womens’ magazine, “How to get love in 10 steps!” it’ll be using 恋愛. But you wouldn’t tell a hot guy ” I 恋愛 you very much!” See?
(こい) Sexual passion.
(おもい) Usually heard in song lyrics. Means, “The one I’m thinking of.” – can be used whether the crush is recirprocal or not. “The one I’m thinking of, I wonder what he’s doing right now?”