How can your cousins be your siblings/parents be your siblings or grandparents?

[William]

It's called incest - the marriage of (or at least reproducing with) close relations.

In the Facebook post you saw, the person's parents were brother and sister. In the song you are referring to, the man's father married his wife's daughter.

Note that divorce or widowing and subsequent remarriage can get around the legal problems that exist with this in most jurisdictions - in the song, the narrator married a widow, and then his father married the widow's daughter who was born before the narrator married the widow. Because of the legal entanglements, his dad is now his stepson-in-law -- making him his own grandpa.