Strength training influences insulin sensitivity in a number of ways. 1) it increases expression and localization of the glut-4 receptor on the skeletal muscle cell thereby allowing glucose to be transported into the muscle cells without insulin, i.e. less insulin is required to clear a given amount of glucose from the blood at this point. 2) Increased skeletal muscle mass allows for a bigger depot of glucose to be stored as glycogen instead of "spilling over" and being converted in the liver to fat to be carried by VLDL. 3) Other things :-)
Reducing carbohydrate intake definitely influences blood lipids, but the changes in sum, are hyper-dependent on what the rest of the diet looks like, weight loss/gain, and other factors. Yea, if you spin down blood after a fatty meal and do the same test the next day fasted things are going to be a lot different, thanks Mike lol.
HIIT does some really cool things, especially if it's actually at a high intensity and high resistance (exercise bike or Wingate sprints FTW). Some research shows you can reduce muscle glycogen stores by 20-40% with one 30s sprint IIRC. You're also contracting the muscles rapidly and at high force too, which can lead to both chemical and architectural changes just like weight training. This is one of the reasons some researchers have found increased strength and power outputs in those who do HIIT.