William Mounce sheds some light on the differences in meaning between the four Greek words for love at the Koinonia blog. For example, about agape:
αγαπαω (αγαπη) [agape] was a colorless word without any great depth of meaning.
Perhaps it is because the word was so colorless that the New Testament writers chose it to express a specifically Christian kind of love, most importantly God’s love for his unlovely creation. All those great talks you have heard about αγαπη [agape] love being an undeserved love for the unlovely really has nothing to do with what the Greek word meant in the Koine. Rather, the word was infused with God’s love and so after the first century carried the biblical nuances of God’s love.
φιλεω [phileo] was the general verb for “love.” It has a wide range of meanings, stretching from hospitality to affection to love, even “to kiss.” It is not necessarily a softened form of love, and is used of God’s love for his Son and our love for God. For example, “the Father loves the Son and shows him all he does” (John 5:20). Paul warns the Corinthians, “If anyone does not love the Lord — a curse be on him” (1 Cor 16:22). Jesus loved Lazarus (John 11:3).