Originally Captain Mar-Vell possessed the normal level of strength for a Kree of his age, height, and build who engaged in intensive regular exercise. Under Earth's gravity he could lift (press) 1000 pounds. His Kree nega-bands enabled Mar-Vell to convert his psionic energy into physical strength, so that he could then lift (press) 10 tons.
Originally, Captain Mar-Vell had no superhumanoid powers. However, the Kree have evolved with greater strength than Earth humans in order to combat the heavier gravity of their home worlds.
The Kree nega-bands converted Mar-Vell's psionic energy into strength (he could now lift 10 tons), a high degree of imperviousness to harm, and the power to fly. They also allowed Mar-Vell to exist unprotected in outer space without having to breathe.
Dr. Benjamin Savannah's radiation treatment altered Mar-Vell genetic structure so that he could absorb solar energy and convert it to various uses. When his solar power was at its peak, Mar-Vell could then lift (press) 15 tons with the nega-bands on. He then relied on the solar power rather than the bands for flight, and would leave a glowing trail behind him.
The exact nature and scope of the "cosmic awareness" granted to Mar-Vell by Eon have never been clearly defined. Apparently it enabled him to sense the presence of beings and objects in the universe that were somehow of importance to him for whatever reason. It may be somewhat comparable to Spider-Man's spider-sense and to Mantis's awareness of psychic "vibrations," but its scope was far greater than either.