I will concentrate on Volume 7 and 10 here, and will cover the other still-in-print volumes (11, 12 and 13) later this week, hopefully. 13 was just released, so I have not yet gotten that one myself, but I will include some information on it as well. (I will eventually review all of the books, but am starting with these.)
NESAT VII was my introduction to this series. I was looking for articles by Michael L. Ryder on sheep evolution and stumbled across this book (which was still available in the hardcover edition on Amazon at the time). I bought it for that article, but there are several others that absolutely helped further my knowledge by introducing me to key researchers. You can still get the Kindle version very inexpensively, or a paperback copy. My favorites are:
Ryder, M.L. "The Human Development of Different Fleece-Types in Sheep and Its Association with the Development of Textile Crafts"
Hedeager Krag, Anne. "Denmark - Europe: Dress and Fashion in Denmark's Viking Age"
Andersson, Eva. "Textile Production at Birka: Household Needs or Organised Workshops"
Rædar Knudsen, Lise. "Brocaded Tablet-Woven Bands: Same Appearance, Different Weaving Technique, Hørning, Hvilehøj and Mammen" (If you are a tablet weaver, you need the chart that accompanies this article.)
NESAT X was the second volume I purchased (before tracking older copies down on ebay or via ILL), and I still refer back to this book frequently as well. You can still get this one in a paperback copy.
Hedeager Krag, Anne. "Oriental Influences in the Danish Viking Age Caftan and Belt with Pouch"
Zubkova, Elena S, Olga V. Orfinskaya, and Kirill A. Mikhailov. "Studies of the Textiles from the 2006 Excavation in Pskov"
I also found a few of the articles on medieval garment construction "Construction and Sewing Technique in Secular Medieval Garments" and "Garments for a Queen" to be very helpful even if they do not relate directly to my Viking studies. This volume is also provides a great start on my Migration era studies with articles on the finds from Tegle and Helgaland, textile crafting in the period and dye analysis from Iron Age Denmark.