You may be thinking of the original Buck Rogers stories Armageddon 2419 A.D. or Airlords of Han.
A version of Armageddon was published in 1978 and was readily available in book stores at the time. It contained the original Armageddon story as well as Airlords of Han.
The premise is that Anthony "Buck" Rogers is trapped in a cave in the 1920s, falls into suspended animation, and awakes 500 years later. When he wakes, he finds that "Mongolians" AKA the Han have taken over the world. Rogers meets a woman named Wilma Deering who is part of a resistance against the Han. Rogers joins the resistance and he and Deering have their adventures.
The world of Buck Rogers includes some technological advances which match your description:
- The rebels have a metal named "inertron" which blocks all forms of energy including gravity. The effect is that inertron has negative weight and can be used to make things float.
- The rebels wear suits with inertron inserts which allow them to jump long distances.
- The rebels have another metal name "ultron" which I believe is extremely tough while being transparent.
- The rebels use inertron and ultron to build armored flying vehicles.
- The bad guys have airships which fly by use of presser beams--energy beams that can push against things. The airships are held up by pushing against the ground, and move by "walking" on the beams.
One thing that Armageddon does not have is aliens, blue-skinned or otherwise. However, following publication of the 1978 edition, Larry Niven and Jerry Pournelle plotted a new series of sequels which were written by other authors:
These stories are set years later. The villians in these stories are the original Han along with an alien race named the Prl'lu. The sequels introduce a new love interest for Rogers named Princess Lu-An. It's possible you're thinking of one of these stories.
Armageddon 2419 A.D. and The Airlords of Han are available on Project Gutenberg.