Let's begin by looking at clue #7: William's wife recently gave Barbara a home permanent. From this, we can conclude that William is not married to Barbara.
Next, lets look at clue #6: The couple who live next door to Gilda and her husband have the same color hair she does, and speak both Spanish and Basque. If John is bald (clue #5), then he does not have the same color hair as Gilda, and thus, cannot live next door to her. If Fred speaks and understands only Basque (clue #4), then he cannot speak or understand Spanish, and thus, he cannot live next door to Gilda. Therefore, if both John and Fred cannot live next door to Gilda, then William must live next door to Gilda. It follows that William is not married to Gilda.
If William is not married to Barbara, and if William is not married to Gilda, it follows that William is married to Gloria. From clue #3, Gloria destroyed the cashmere sweater!