They all may mean "to get, to receive" and in that sense there is no real difference: "Ich habe Ihr Paket/Ihre Nachricht erhalten/bekommen/empfangen." Of the three, "empfangen" is least often used. However, "erhalten" also means "to maintain, to preserve (e.g. old buildings), "empfangen" also means "to welcome, to receive" as in "Das Brautpaar empfing die Gäste" (the guests were received by the bridal couple), and if you're talking about a pregnant woman, you say "sie bekommt ein Kind" (not: erhält or empfängt).

Danke!! =D

Edith: "ein Kind empfangen" = to conceive (and therefore not at all the same as "ein Kind bekommen")